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Hewitt E., Ross K.A. - Abstract Harmonic Analysis (Vol. 1) :: Электронная библиотека попечительского совета мехмата МГУ
 
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Hewitt E., Ross K.A. - Abstract Harmonic Analysis (Vol. 1)
Hewitt E., Ross K.A. - Abstract Harmonic Analysis (Vol. 1)

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Название: Abstract Harmonic Analysis (Vol. 1)

Авторы: Hewitt E., Ross K.A.

Аннотация:

Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory.A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1979

Количество страниц: 519

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$mathfrac{D}(n)$      7
$mathfrac{D}(n)$ is compact      29
$mathfrac{D}(n)$ is locally Euclidean      29 -31
$M_a$      269
$M_a$ has approximate unit      303
$M_a$ has no unit      303
$M_a$, commutative if and only if G is      302
$M_a$, ideals characterized      303
$M_a$, isomorphic with $\mathfrak{L}_1$      272
$\alpha$-mesh      13
$\delta$-topology      360
$\Delta_a$      109 416-417
$\Delta_a$, character group of      402
$\Delta_a$, Haar measure on      202
$\Delta_p$      109
$\Delta_p$, automorphism group of      434
$\Delta_p$, minimal divisible extension of      419
$\iota$-almost everywhere      124
$\iota$-measurable function      125
$\iota$-measurable set      125
$\iota$-null function      124
$\iota$-null set      124
$\matfrak{G}\matfrak{L}(n, F)$      7
$\matfrak{G}\matfrak{L}(n, F)$ has inequivalent uniform structures      28-29
$\matfrak{G}\matfrak{L}(n, F)$ is locally Euclidean      29-31
$\matfrak{G}\matfrak{L}(n, F)$, Haar measure on      201 209
$\matfrak{G}\matfrak{L}(n, F)$, left invariant metric on      78
$\mathbb{Q}$ (rational numbers)      3
$\mathbb{Q}$, character group of      404 414
$\mathbb{R}$ (real line)      3
$\mathbb{R}$ is open continuous homomorph of totally disconnected group      50
$\mathbb{R}$, automorphism group of      433
$\mathbb{R}$, character group is R      367
$\mathbb{R}$, compact connected topology for      415
$\mathbb{R}$, continuous homomorphisms of      370
$\mathbb{R}$, Haar measure on      198
$\mathbb{R}$, invariant mean for $\mathfrak{U}(R)$      256
$\mathbb{R}$, invariant means for $\mathfrak{B}^r(R)$      240
$\mathbb{R}$, topologies in      27
$\mathbb{R}^n$      3
$\mathbb{R}^n$, automorphism group of      434
$\mathbb{R}^n$, characterized      104
$\mathbb{R}^n$, closed subgroups of      92
$\mathbb{Z}$ (integers)      3
$\mathbb{Z}$, character group is T      366
$\mathbb{Z}$, invariant mean for $\mathfrak{U}(Z)$      256
$\mathbb{Z}$, nondiscrete topology for      27
$\mathfrak{G}_0^{\ast}(G)$ as convolution algebra      265
$\mathfrak{G}_0^{\ast}(G)$, adjoint operation in      299
$\mathfrak{G}_0^{\ast}(G)$, equivalent with M{G)      269
$\mathfrak{G}_{00}(G)$      119
$\mathfrak{G}_{00}(G)$, nonnegative linear functionals on      120
$\mathfrak{G}_{00}(G)$, unbounded linear functionals on      167
$\mathfrak{L}_1(G)$, isomorphic with $M_a$      272 (see also 'M_a(G)$')
$\mathfrak{S}\mathfrak{D}(n)$      7
$\mathfrak{S}\mathfrak{D}(n)$ is compact      29
$\mathfrak{S}\mathfrak{D}(n)$ is locally Euclidean      29-31
$\mathfrak{S}\mathfrak{L}(n, F)$      7
$\mathfrak{S}\mathfrak{L}(n, F)$ has inequivalent uniform structures      28-29
$\mathfrak{S}\mathfrak{L}(n, F)$ has no finite-dimensional unitary representations      350
$\mathfrak{S}\mathfrak{L}(n, F)$ is locally Euclidean      29-31
$\mathfrak{S}\mathfrak{L}(n, F)$, homomorphisms into