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Duistermaat J.J, Kolk J.A.C. - Distributions: theory and applications
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Название: Distributions: theory and applicationsАвторы: Duistermaat J.J, Kolk J.A.C. Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: book draftГод издания: 2006Количество страниц: 300Добавлена в каталог: 07.10.2012Операции: Положить на полку |
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Предметный указатель
32 154 14 Absorbing sequence 60 Almost everywhere 31 Analytic continuation 124 Analytic function 15 Analytic singular support 116 Arzela - Ascoli theorem 5 Averaging with weight function 6 Backward cone 126 Banach space 103 Banach - Steinhaus theorem 44 Basis 62 Basis, dual 74 173 beta function 134 Binomial coefficients 19 Bolzano - Weierstrass theorem 13 Bounded linear mapping 63 Calculus of variations 3 Capacitor 80 Cauchy formula problem, uniqueness 131 Cauchy integral formula 115 Cauchy integral theorem 114 Cauchy problem, existence 192 Cauchy - Riemann operator 116 Chain rule 49 Characteristic function 21 Closure 2 Compact 11 Completeness 211 Completeness of 44 Completion 211 complex derivative 113 Complex line integral 114 Complex-analytic 115 Complex-analytic family of distributions 124 Complex-analytic function, distribution-valued 124 Complex-analytic in several variables 116 Complex-differentiable 113 Complex-differentiable distribution 113 composition 50 Cone, backward 126 Cone, forward 126 Connected 15 Continuity of linear form 27 continuous 62 Continuous, Hoelder 206 Continuous, sequentially 62 Continuous, - inclusion 144 Continuous, - linear form 59 Continuous, - linear mapping 62 Convergence in 59 Convergence in 19 Convergence in 43 Convergence in 59 Convergence in 150 Convergence in 144 Convergence of distributions 43 Convergence, weak 63 Convex 61 198 Convex, locally 61 Convolution 7 Covering, open 11 Cut-off function 21 Dense 60 Density of measure 34 Derivative in direction of outer normal 118 Derivative of distribution 39 Derivative, complex 113 Derivative, total 49 Determinant, Jacobi 79 Diffeomorphism 78 Differentiable family 81 Diffusion equation 45 Dipole vector 118 Dirac function 32 Dirac notation 32 Direct product 96 Dirichlet kernel 259 Dirichlet problem 119 Discrete 58 distribution 27 Distribution with compact support 64 Distribution, complex-differentiable 113 Distribution, derivative of 39 Distribution, extension of 54 Distribution, homogeneous 83 Distribution, multiperiodic 173 Distribution, order of 33 Distribution, periodic 87 Distribution, positive 34 Distribution, potential of 110 Distribution, reflected 80 Distribution, restriction of 53 Distribution, support of 54 Distribution, tempered 150 Distribution-valued complex-analytic function 124 Distributional extension 54 Distributional, sense, in 6 Distributional, solution of Cauchy problem 132 Distributions, convergence of 43 Divergence 1 Divergence theorem 2 Dual basis 74 173 Dual lattice 173 Dual, topological 28 63 Elliptic operator 180 Embedding 84 Equation, diffusion 45 Equation, Euler's differential 83 Equation, heat 45 Equation, Helmholtz' 120 Equation, Poisson's 110 Equations of Euler - Lagrange 4 Euler differential equation 83 Euler - Lagrange, equations of 4 Evaluation 32 Expectation 35 Extension of distribution 54 Family of distributions, complex-analytic 124 Family, differentiable 81 Fiber, integration over 86 Flow 82 Form, continuous linear 59 Form, linear 27 Form, monotone linear 35 Formula, Cauchy's integral 115 Formula, Fourier's inversion 149 Formula, Green's 119 Formula, Parseval's 149 Formula, Poisson's summation 171 Formula, Poisson's summation, in 174 Formula, Pompeiu's integral 115 Formula, Radon's inversion 165 Formulas, Sokhotsky's 221 Forward cone 126 Fourier coefficient 167 Fourier integral operator 198 Fourier inversion formula 149 Fourier series in 170 Fourier transform 142 Fourier - Laplace transform 144 Function, analytic 15 Function, Beta 134 Function, characteristic 21 Function, complex-analytic 115 Function, complex-analytic in several variables 116 Function, complex-differentiable 113 Function, cut-off 21 Function, Dirac 32 Function, distribution-valued complex-analytic 124 Function, Gamma 132 Function, harmonic 110 Function, Heaviside 40 Function, moment of 52 Function, rapidly decreasing 144 Function, real-analytic 116 Function, Riemann's "nondifferentiable" 46 Function, square-integrable 154 Function, support of 15 Function, test 15 Function, translated 7 Functional analysis 28 Functional, linear 27 Fundamental domain 173 Fundamental matrix 71 Fundamental solution 109 Gamma function 132 Gauss density 23 Green's formula 119 Group law 82 Hahn - Banach theorem 153 Harmonic 110 Heat equation 45 Heaviside function 40 Heine - Borel theorem 13 Helmholtz equation 120 Hilbert space 154 Hilbert transform 158 Hoelder continuous 206 Homogeneous distribution 83 Homotopy 134 Huygens principle 131 Hyperbolic operator 197 Hypoelliptic 111 In distributional sense 6 In weak sense 6 Inclusion, continuous 144 Increasing 60 Independent sum of probability measures 106 Inequality, Young's 106 Integer part 176 Integrable, locally 22 30 Integral kernel 112 Integral norm 103 Integral, complex line 114 Integral, Riemann - Liouville 126 Integration over fiber 86 Integration under distribution sign 93 Integration, Lebesgue 22 Integration, Riemann 22 Invariant, as density 83 Invariant, as generalized function 83 Inverse function theorem 78 Jacobi determinant 79 Jacobi, matrix 79 Jump relations 264 Kernel, Dirichlet 259 Klein - Gordon operator 199 Laplace operator 42 Laplace transform 144 Lattice 173 Lattice, dual 173 Layer 54 Layer, double 80 Layer, multiple 81 Lebesgue integration 22 Leibniz' formula 19 Leibniz' rule 19 Lemma, Weyl's 112 Lie group 175 Linear form 27 Linear form, continuous 59 Linear form, monotone 35 Linear functional 27 Linear mapping, bounded 63 Linear mapping, continuous 62 Linear partial differential operator 56 Liouville theorem 184 Locality property 215 Locality property, weak 215 Localization at infinity 215 Locally convex 61 Locally in 203 Locally integrable 22 30 Lorentz group 127 Mapping, bounded linear 63 Mapping, continuous linear 62 Mapping, proper 77 Mapping, sum 96 Matrix, fundamental 71 Matrix, Jacobi 79 Mean of 173 Mean, of distribution 168 Mean, of function 167 Measurable set 23 Measure 34 Measure, density of 34 Measure, Dirac 34 Measure, point 32 Measure, positive 35 Measure, probability 35 Measure, Radon 34 minimizing 4 Moderate growth 169 Moderate growth, multisequence of 173 Modulo 111 Mollifier 8 Moment of function 52 Momentum operator 145 Monotone linear form 35 Multi-index 18 Multi-index, order of 18 Multiperiodic 173 Multisequence of moderate growth 173 Neighborhood 61 Norm, integral 103 Open covering 11 Operator commuting with translations 92 Operator, Cauchy - Riemann 116 Operator, elliptic 180 Operator, Fourier integral 198 Operator, hyperbolic 197 Operator, Klein - Gordon 199 Operator, Laplace 42 Operator, linear partial differential 56 Operator, momentum 145 Operator, position 70 Operator, pseudo-differential 182 Operator, singular integral 112 Operator, wave 113 Orbit 128 Order of distribution 33 Order of multi-index 18 Paley - Wiener theorem 190 Parametrix (distribution) 111 Parametrix, as operator 112 Parseval formula 149 Partition of unity 20 Periodic distribution 87 Plane wave 141 Point measure 32 Point source 2 Point, stationary 57 Poisson equation 110 Poisson summation formula 171 Poisson summation formula in 174 Polynomial, Taylor 51 Pompeiu integral formula 115
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