Curriculum vitae

Serguei Piskarev, Ph.D.

Leading scientific fellow

Science Research Computer Center of Moscow State University,

Vorobjevy Gory, Moscow 119899, Russia

Tel. Office 7 - 095 - 939-53-12

Tel. Home 7 - 095 - 191-53-12

Fax 7 - 095 - 191-53-12

e-mail piskarev@tarski.math.usf.edu

e-mail piskarev@math.uni-karlsruhe.de

e-mail s_piskarev@hotmail.com

e-mail serguei@piskarev.srcc.msu.ru

e-mail piskarev@srcc.msu.ru

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Personal

Date of birth: 14.01.1953

Place of birth: Kostroma City, Russia

Marital Status : Married since 1982, one beautiful daughter.

Education

1989: Diploma of Senior Research Fellow. USSR Academy of

Science.

1981 (September): Ph.D. in Mathematics, Mathematical Institute of

Academy of Science in Minsk, USSR. My supervisor was Professor G.M. Vainikko.

1976 - 1979: Postgraduate studies. Department of mathematics, Tartu State University,

Estonia.

1976: (M.Sc.) in Mathematics, Tartu State University, Estonia.

1971 - 1976: (BA) Department of mathematics, Tartu State University,

Estonia.

Professional Experience

1994 - nowadays. Leading scientific fellow. Science Research Computer Center,

Moscow State University, Vorobjevy Gory, Moscow 119899, Russia

19.12.1994 - PRESENT.

2001 - 2002. VISITING PROFESSOR. Department of Mathematics, University

of Karlsruhe. DAAD grant system. Karlsruhe, Germany

2001 - 2001. VISITING PROFESSOR. Institute of Systems Science. Chinese Academy of Science. Beijing 100080, P.R. China

2000 - 2000. RESEARCH VISITOR. Department of mathematics, University of New South Wales, Sydney, Australia.

2000 - 2000. RESEARCH VISITOR. Department of Mathematics, The University of Queensland, Brisbane Qld 4072, Australia.

1999 - 2000. VISITING PROFESSOR. Department of mathematics, University of South Florida, Tampa, Florida 33620, USA

1999 - 1999. RESEARCH VISITOR. Department of mathematics, University of New South Wales, Sydney, Australia

1999 - 1999. VISITING SCHOLAR. Department of Mathematics, The University of Queensland, Brisbane Qld 4072, Australia.

1998 - 1998. RESEARCH VISITOR. Department of mathematics, Bar-Ilan University, Bar-Ilan, Israel.

1997 - 1997. VISITING SCHOLAR. Department of mathematics, The University of Queensland, Brisbane Qld 4072, Australia.

1997 - 1997. VISITING PROFESSOR. Department of mathematics, Middle East Technical University, 06531 Ankara, Turkey.

1996 - 1997. RESEARCH VISITOR. Department of mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China.

1996 - 1996. VISITING PROFESSOR. Department of mathematics, Kyungam

University, Masan, 631-701 Korea.

1996 - 1996. VISITING SCHOLAR. Department of Mathematics and Computer Science,

University of Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium.

(24.01.1996 - 24.07.1996).

1996 - 1996. VISITING PROFESSOR. Department of mathematics, University of

Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy.

1995 - 1995. VISITING SCHOLAR. Department of Mathematics, Science

University of Tokyo, Wakamiya-Cho 26, Shinjuku-Ku, Tokyo 162, Japan.

1995 - 1995. VISITING PROFESSOR. Department of Numerical Analysis, Jean Monnet

University, 23, rue du docteur Paul Michelon, St-Etienne 42023, France.

1994 - 1994. VISITING PROFESSOR. Department of mathematics, Middle East

Technical University, 06531 Ankara, Turkey.

1994 - 1994. VISITING PROFESSOR. Department of mathematics, University of Bologna,

Piazza di Porta S. Donato 5, 40127 Bologna, Italy.

1994 - 1994. VISITING PROFESSOR. Department of mathematics, Ohio University, Athens,

Ohio 45 701, USA.

1992 - 1994. RESEARCH VISITOR. Department of mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China.

1991 - 1992. RESEARCH VISITOR. Department of mathematics, Lulea University of Technology, Lulea, Sweden.

1991 - 1991. RESEARCH VISITOR. Department of mathematics, Chalmers University, Goteborg, Sweden.

1991 - 1994. CHAIRMAN OF LABORATORY, Senior research fellow. Scientific-Industrial Center "Ecologos", ul. Novoscukinskaja 7, Moscow 123 098, Russia.

1990 - 1991. POSTDOCTORAL ASSISTANT. Mathematical Institute of University of Zurich,

Zurich, Switzerland.

1990 - 1991. CHAIRMAN OF LABORATORY. Senior research fellow. The Inter Branch Research Center "Natural Resources", The State Committee on Invention and Discoveries, Moscow.

1984 - 1990. SENIOR RESEARCH FELLOW. Acoustic institute Academy of Science of USSR, Moscow. A diploma of senior research fellow awarded in 1989 by USSR Academy of Science.

1982 - 1984. CHAIRMAN OF LABORATORY , Senior research fellow. All Union Scientific Research and Projected Institute of Automate Control Systems, Moscow.

1979 - 1982. ASSISTANT. Department of mathematical simulations. All Union Scientific Research Institute on Energy and Oil Problems, Moscow.

Scientific Activities

Author and co-author of more than 60 research papers and communications in

scientific journals, conference proceedings and special issues.

I was the translator into Russian in Mir Publishers of the following

books :

1. Clement Ph., Heijmans H.J.A.M., Angenent S., van Duijn C.J., de Pagter B.

One-parameter Semigroups. North-Holland, 1987.

2. Hess P. Periodic-parabolic boundary value problems and positivity.

Pitman. 1991.

Participant and speaker of many international conferences on the subject on semigroups of operators and evolution equations:

Functional Analytic Methods for Structured Population Models, Holland (1990);

Differential Equations in abstract spaces, Bologna, Italy (1991); 3rd International

Workshop-Conference on Evolution Equations, Control Theory and Biomathematics,

Han-sur-Lesse, Belgium(1991); Evolution Equations Conference, Baton Rouge, USA(1993);

28th Annual Meeting of the Mathematical Society of the Republic of China (1992); Sino-Australian Joint Workshop on Nonlinear Analysis, Taiwan (June, 1993); Workshop on Nonlinear Analysis, Shi-Tou, Taiwan (July, 1993); 19th International Conference on Evolution Equations and Applications, Tokyo, Japan (December 21-23, 1993); Fourth Workshop-miniconference on Operator Theory and Evolution Equations, Baton Rouge, USA (March, 1994); Evolution Equations Conference, Glasgow, UK (July, 1994); Conference on Evolution Equations and Semigroups, Pisa, Italy (September, 1994); American Mathematical Society - BeNeLux Congress, Antwerpen, Belgium ( May, 1996); Workshop on Partial Differential Equations, Han sur Lesse, Belgium ( June, 1996); The second International conference on Nonlinear Functional Analysis and Applications,

Masan, South Korea ( August, 1996 ); Annual Meeting of Mathematical Society of Korea, Seuol, South Korea (October, 1996); Fifth International Conference on Evolution Equations and Their Applications to Technology, Hiroshima, Japan (October, 1996); Applied Mathematical Analysis Conference 97 (Including Optimization ` Control), Kaohsiung Polytechnic Institute, Taiwan (January, 1997); International Conference "Function spaces. Differential operators. Problems of mathematical education", Moscow, Russia (March, 1998);3rd European Congress of Mathematics, Barselona (July, 2000); International Conference on Differential Equations and Dynamical Systems, Suzdal, Russia (August, 2000); 4th International Conference on Functional Analysis and Approximation Theory, Maratea, Italy (September, 2000); International conference on Computational Stochastic Differential Equations, Warwick, UK (March, 2001); TULKA miniconference, Karlsruhe, Germany (December, 2001); Conference on Morden Methods in the Theory of Boundary Problems, Voronezh, Russia (May, 2002);

Presentations and Lectures

University of Essen ( Essen, Germany), University of Tubingen ( Tubingen, Germany), Waseda University (Tokyo, Japan), University of Los-Angeles (UCLA, USA), Institute of Mathematics, Taiwan Academy of Science (Taipei, Taiwan), University of South Florida (Tampa, USA), Bilkent University (Ankara, Turkey), Stockholm University ( Stockholm, Sweden), Brunel University (London, UK), Ohio University (Athens, USA), Saitama University (Tokyo, Japan), Charles University of Prague ( Prague, Czech), Institute of Analysis ( Dresden, Germany), Technical University of Delft (Holland), Center for Mathematics and Computer Science (Amsterdam, Holland), University of Antwerpen (Belgium), University of Valladolid ( Valladolid, Spain), University of Poitiers ( Poitiers, France), University of Valencia ( Valencia, Spain), University de Franche-Comte (Besancon, France), University Claude Bernard Lyon 1 (France), Ochanomizu University (Tokyo, Japan), Osaka University (Osaka, Japan), University of

Ellectro-Communications (Tokyo, Japan), Chubu University (Kasugai, Japan), Stefan Banach International Mathematical Center (Warsaw, Poland), Jean Monnet University ( St-Etienne, France), Universite' des Sciences et Technologies de Lille ( Lille, France), Universitat Innsbruck ( Innsbruck, Austria), Universitat Augsburg ( Augsburg, Germany), University of Valenciennes ( Valenciennes, France), University of Tokyo (Tokyo, Japan), Normal University of Taipei (Taipei, Taiwan), National Changhua University of Education ( Changhua Sity, Taiwan), Chung Yuan University ( Chung-Li, Taiwan), Research Center of Applied Mathematics, Selcuk University (Konya, Turkey), School of Mathematics, University of New South Wales ( Sydney, Australia ), School of Mathematics and Statistics, The University of Sydney ( Sydney, Austarlia ), Department of Mathematics, Bar-Ilan University (Ramat Gan, Israel), Department of mathematics, University of Tel-Aviv (Tel-Aviv, Israel), Department of Mathematics, University of Adelaide (Adelaide, South Australia), School of Mathematical Sciences, Australian National University (Canberra, Australia), Department of Mathematics, University of Science and Technology of China ( Hefei, Anhui, P. R. China), niversity of Twente (Hengelo, Holland), University of Antwerpen (Antwerp, Belgium), University of Karlsruhe (Karlsruhe, Germany), University of Augsburg (Augsburg, Germany), Johann Wolfgang Goethe University (Frankfurt, Germany), University of Hannover (Hannover, Germany),

Publications

S. PISKAREV

BOOKS and BOOKCHAPTERS

Piskarev S.I., Vasiliev V.V. Differential Equations in Banach Spaces I. Semigroup Theory. Moscow State University Publish House (in Russian), 1996, 164 p.

Piskarev S.I., Vasiliev V.V. Differential Equations in Banach Spaces. Theory of Cosine Operator-Functions. Moscow State University Publish House ( in preparation) (in Russian).

Piskarev S. On calibration of the inter-branch economical balance models. The problem of planing and development of TEK of the state in nowadays. Moscow, 1981, p. 131-132.

Vasiljev V.V., Krein S.G., Piskarev S.I. Semigroups of operators, cosine operator functions and linear differential equations. Progress in Science and Technology. Mathematical analysis, Vol. 28, p. 87 - 204, 1990.

ARTICLES in refereed JOURNALS and PROCEEDINGS

1. Piskarev S. Convergence of the spectrums of the operator-values functions. Conference of a Humanities and Natural science of Baltic republics and Byelorussia, Tartu, 1976, p. 100-101.

2. Piskarev S. On approximation of essential spectrum of holomorphic operator-valued functions. Proceedings of students scientific society, Tartu, p. 79-87.

3. Piskarev S. On compact convergence of resolvents and semigroups. Proceedings of conference "Algebraic and functional analysis methods in operator research", 1978, p. 71-74.

4. Piskarev S. Compact convergence in semidiscrete approximations of differential equations of first and second orders. Conference " Asymptotic methods in the theory of singular perturbation of equations II". Alma-Ata, 1979, p. 56-58.

5. Vainikko G.M., Piskarev S.I. On regular consistent operators. Izvestia vys$\check{s}$., ucebnyh Zavedenii (VUZ), Matematika, 1977, N 10 (185), p. 25-36.

6. Piskarev S. On approximation of holomorphic semigroups. Tartu, Riikl. Ul. Toimetised, 1979, N 492, p. 3-23.

7. Piskarev S. Discretisation of abstract hyperbolic equation. Ucheb. zapiski Tartuskogo Gos. Universiteta, 1979, N 500, p. 3-23.

8. Piskarev S. Solution of an inhomogeneous abstract linear hyperbolic equation. Ucheb. zapiski Tartuskogo Gos. Universiteta, 1979, N 500, p. 24-32.

9. Piskarev S. Error estimates for approximation of semigroups of operators by Pade's fractions. Izvestia vys$\check{s}$.,\rm ucebnyh Zavedenii, Matematika, 1979, N 4 (203),

p. 33-38.

10. Piskarev S. On discretisation of hyperbolic equation. " Numerical treatments in bounded value and integral equations". Tartu, 1981, p. 26-28.

11. Piskarev S. Periodic and almost periodic cosine operator functions. Mat. Sbornic, Nov. Ser., 1982, 118 (160), p. 386-398.

12. Piskarev S. Compact convergence for the approximation of differential equations in a Banach space. Ucheb. zapiski Tartuskogo Gos. Universiteta, 1983, N 633, p. 11-18.

13. Piskarev S. On estimates for the rate of convergence in semidiscretisation of evolution equations. Differential Equations, 1983, 19, N 12, p.2153-2159.

14. Piskarev S. Almost periodic solutions of second order differential equations. Siberian Math. Journal, 1984, 25, N 3, p. 137-147.

15. Piskarev S. On stability of difference schemes in Cauchy problems with almost periodic solutions. Differential Equations, 1984, 20, N 4, p. 689-695.

16. Piskarev S. Solution of second order evolution equations under Krein-Fattorini's conditions. Differential Equations, 1985, 21, N 9, p. 1602-1612.

17. Piskarev S. Increasing of the accuracy of the approximation in solving of initial problems. Proceedings of the Conference "Methods of solution of integral, differential and operator equations", Tartu, 1987, p. 18-20.

18. Piskarev S. Estimates of rate of convergence in the case of solution of ill-posed problems for evolution equations. Izvestija Akad. Nauk USSR, Ser. Math., 1987, vol. 51, N 3, p. 678-687.

19. Piskarev S. Splitting of the spectrum of symmetrical matrix. Proceedings of the conference "Numerical methods in modern wave acoustics problems." Moscow, 1988, p. 59.

20. Piskarev S. On method of solution of Helmholtz equation in stratified ocean without absorption. Proceedings of the conference " Methods of algebra and analysis", Tartu, 1988, p. 187-188.

21. Piskarev S. A method of increasing the accuracy of the solution of initial problems in Banach space. USSR. Comput. Math. Phys., 1988, 28, N 6, p. 211 - 212.

22. Piskarev S. Convergence of difference schemes for the solution of nonlinear parabolic equations. Math. Zametki, 1988, Vol. 44, N 1, p. 112-123.

23. Piskarev S., Piskunov D. Application of the method of conjugate gradients to adaptive spatial filtering. Soviet Journal of Comm. Technology and Electronics., 1990, 35, N 5, p. 17 - 25.

24. Piskarev S. Approximation of positive $C_0$-semigroups. Differen. Uravnenija, 27, N 7, p.1245 - 1250, 1991.

25. Piskarev S. Compactness properties in the theory of the cosine operator functions. Mathemat. Zametki, 1992, Vol. 51, N 5, p. 151 - 153.

26. Crouzeix M., Larsson S., Piskarev S., Thomee V. The stability of rational approximations of analytic semigroups. BIT, 1993, Vol. 33, p. 74 - 84.

27. Piskarev S. Rational approximations of analytic semigroups. Proc. of 3rd International Workshop-Conference on Evolution Equations, Control Theory and Biomathematics. Belgium, "Han-sur-Lesse, October 20-26, 1991", p. 467-471, Marcel Dekker, Inc., 1993.

28. Piskarev S., Shaw S.-Y. Multiplicative perturbations of $C_0$-semigroups and applications to step responses and cumulative outputs. J. Funct. Anal., 1995, 128, N2, p. 315-340.

29. Piskarev S., Shaw S.-Y. On some properties of step responses and cumulative outputs. Chinese J. Math., 1994, Vol. 22, No. 4, p. 321-336.

30. Piskarev S., Shaw S.-Y. Asymptotic behavior of some functions related to $C_0$-semigroups of operators. Saitama J. Math., 1994, 12, p. 7 - 12.

31. Piskarev S., Shaw S.-Y. Perturbation and Comparison of Cosine Operator Functions. Semigroup Forum, 1995, 51, p.225-246.

32. Piskarev S. On approximation of perturbed $C_0$-semigroups. Differential Equations (in Russian), 1994, 30, 2, p. 339-341.

33. Piskarev S., Shaw S.-Y. Perturbation of cosine operator functions by step response and cumulative output, to appear in the Proceedings of the Conference on Evolution Equations, University of Strathclyde, July 25-29, 1994.

34. deLaubenfels R., Piskarev S. The growth rate of cosine families. J. Math. Anal. and Appl., 1995, 196, p. 442-451.

35. Ergen\c{c} T., Karas\"ozen B., Piskarev S. Approximation for semilinear Cauchy problems involving second order equations in separable Banach spaces. Nonlinear Anal. Theory,

Meth. and Appl., 1997, Vol 28, p. 1157-1165.

36. Piskarev S., Shaw S.-Y. On certain operator families related to cosine operator functions. Taiwanese J. Math., 1997, 1, p. 527-546.

37. Guidetti D., Piskarev S. On maximal regularity stability of difference schemes for parabolic equations in $C^\theta(\Omega)$ spaces. Preprint, Department of mathematics, University of Bologna, N 8, 1997.

38. Bobylev N.A., Kim J.K., Korovin S.K. and Piskarev S. Semidiscrete approximations of semilinear periodic problems in Banach spaces. Nonlin. Anal. Meth. Theory and Applications, 1998, Vol. 33, No.5, p. 473-482.

39. Guidetti D., Piskarev S. "On maximal regularity of Crank-Nicolson schemes for parabolic equations in $C^{\theta}(\overline \Omega)$ space". Proceedings of International Conference "Function spaces. Differential operators. Problems of mathematical education", Vol.2, p.217 - 222, Moscow: RUDN, 1998.

40. D. Guidetti, S. Piskarev, "Stability of Rothe's scheme and maximal regularity for parabolic equations in $C^{\theta}(\overline \Omega)$", in "Progress in partial Differential Equations", Pont-\'a-Mousson 1997, vol. 1 (ed. H. Amann, C. Bandle, M. Chipot, F. Conrad, I. Shafrir), Pitman Research Notes in Math. 383 (1998).

41. M. Ahues, S. Piskarev Spectral approximation of weakly singular integral operators. I: Convergence theory. Integral methods in science and engineering. Vol. II: Approximation methods. Proceedings of the 4-th international conference, IMSE '96, Oulu, Finland, June 17-20,

1996. Harlow: Longman. Pitman Res. Notes Math. Ser. 375, 35-39 (1997).

42. Guidetti D. Piskarev S. Stability of the Crank-Nicolson scheme and maximal regularity for parabolic equations in $C\sp \theta(\overline\Omega)$ spaces. Numer. Funct. Anal. Optim. 20

(1999), no. 3-4, 251--277.

43. Chyan D.-K. Shaw S.-Y., Piskarev S. On maximal regularity and semivariation of cosine operator functions. (English. English summary) J. London Math. Soc. (2) 59 (1999), no. 3, 1023--1032.

44. Burrage K., Piskarev S. Stochastic methods for ill-posed problems. BIT, 2000, Vol. 40, N 2, pp. 226 - 240.

45. V. V. Vasilev, S.I. Piskarev. Bibliography on Differential Equations in Abstract Spaces. Moscow State University, 2001, Electronic journal.

( http://www.srcc.msu.ru/num_anal/list_wrk/page_5u.htm )

PostScript (1115,2 Kb) PostScript.zip (336,1 Kb)

46. Palencia C., Piskarev S. On the Multiplicative perturbations of $C_0$-groups and $C_0$-cosine operator functions. Semigroup Forum, 2001, Vol. 63, N 2, p. 127-152.

NONREFEREED PUBLICATIONS and REPORTS

1. Piskarev S.I., Krasinskii P.J., Piskunov D.A. et el. Report N AK - 3514. Acoustic Institute, Academy of Science, USSR, 1985.

2. Piskarev S.I., Kuznecova T.A. Report N AK - 8515. Acoustic Institute, Academy of Science, USSR, 1985.

3. Piskarev S.I., Krasinskii P.J., Piskunov D.A. et el. Report N AK - 8610. Acoustic Institute, Academy of Science, USSR, 1986.

4. Piskarev S.I., Rozhkov Ju.S. et el. Report N AK - 8683. Acoustic Institute, Academy of Science, USSR, 1986.

5. Piskarev S.I., Krasinskii P.J., Piskunov D.A. et el. Report N AK - 9278. Acoustic Institute, Academy of Science, USSR, 1986.

6. Piskarev S.I. Principles of discretisation methods I. Report N AK - 3298. Acoustic Institute, Academy of Science, USSR, 1986, 76 p.

7. Piskarev S.I. Principles of discretisation methods II. Report N AK - 3339. Acoustic Institute, Academy of Science, USSR, 1986, 101 p.

8. Piskarev S.I. Principles of discretisation methods III. Report N AK - 3410. Acoustic Institute, Academy of Science, USSR, 1986, 87 p.

9. Piskarev S.I.,Krasinskii P.J., Piskunov D.A. Article. Sudostr. Promyslennost'. Acoustics, Vyp. 13, 1987, p. 13- 17.

10. Piskarev S.I., Studenicnik N.V., Kirilenko B.G., Pirogov V.Ju. et el. Report N AKIN - 9739. Acoustic Institute, Academy of Science, USSR, 1987.

11. Piskarev S.I. Principles of discretisation methods IV. Report N AKIN - 3478. Acoustic Institute, Academy of Science, USSR, 1987, 129 p.

12. Piskarev S.I. Principles of discretisation methods V. Report N AKIN - 3587. Acoustic Institute, Academy of Science, USSR, 1988, 104 p.

13. Piskarev S. Approximation of nonlinear equations in Banach spaces. Proceedings of the Conference on the Theory of Operators in Functional Spaces. Kuibyschev, 1988, p.148 - 149.

14. Piskarev S., Piskunov D. Adaptive spatial filtering and simulations. Report N AKIN - 3617, 1988, 194 p.

15. Piskarev S.I., Tujilkin Ju.I., Baronkin V.M., Popov R.Ju. Report N AK - 10285. Acoustic Institute, Academy of Science, USSR, 1988.

16. Piskarev S. Article. Sudostr. Promyslennost'. Ser. Acoustics, 1989, Vyp. 34.

17. Piskarev S.I., Tujilkin Ju.I., Gelfgat V.I., Leikin D.E. et el. Report N P-161. Acoustic Institute, Academy of Science, USSR, 1989.

18. Piskarev S. Compact approximation of resolvents. Preprint. Zurich, 1991.

19. van Casteren J., Piskarev S. and Shaw S.-Y. Discretisation of $C$-semigroups. Proceedings of the Conference on Inverse and ill-posed problems. Moscow State University, Moscow , 1998, p.18 .

20. Guidetti D., Karasozen B. and Piskarev S. Approximation of abstract differential equations. 2001, Electronic journal. To get the whole paper send the command "get evolve-l 01-00036" to the following e-mail address: listserv@uni-karlsruhe.de Instead you may get the paper at

"http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html"

21. Ashyralyev A., Piskarev S.I. and Weis L. On well-posedness of difference schemes for abstract parabolic equations in $L^p([0,T];E)$ spaces. Proc. Voronezh Spring School "Pontrjagin's lectures-XIII", p. 9-10, 2002.

PUBLICATIONS SUBMITTED

1. van Casteren J., Piskarev S. and Shaw S.-Y. Discretisation of $C$-semigroups. Subm. to Inverse and Ill-posed Problems.

2. Kantorovitz S., Piskarev S. Mean stability of semigroups and cosine operator functions. To appear in Taiwanese Journal of Mathematics.

3. Jefferies B., Piskarev S. Tauberian theorems for semigroups. To appear in Proceedings of Maratea conference.

4. Jefferies B., Piskarev S. Tauberian theorems for cosine operator functions. Submitted to Proceedings of Steklov Institute.

5. Guidetti D., Piskarev S. Some remarks on real interpolation and finite differences. Submitted to Abstract and Applied Analysis.

6. Takenaka T., Piskarev S. Local $C$-cosine families and local integrated cosine families. Subm. To Taiwan J. of Math.

7. Ashyralyev A., Piskarev S., Weis L. On well-posedness of difference schemes for abstract

parabolic equations in $L^p([0,T];E)$ spaces. Subm. To Numerical Functional Analysis and Optimization.

8. Li Miao , Guo B.-Z. and Piskarev S. Compactness and norm continuity of the difference of two cosine functions. Subm. To Taiwaness Journal of Mathematics.

9. Guidetti D., Karasozen B. and Piskarev S. Approximation of abstract differential equations. Subm. To VINITI survey.

Achievements, Fields of Interest

My fields of scientific interests mostly contain theory of semigroups of operators, cosine operator-function theory, differential equations in Banach spaces, numerical analysis in linear and semilinear differential equations in abstract spaces, approximation of the spectrum of operators. For more detail comments please look at