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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: Рубрика: Математика /Анализ /Продвинутый анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: Second EditionГод издания: 1979Количество страниц: 519Добавлена в каталог: 02.04.2005Операции: Положить на полку |
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Предметный указатель
Subgroup, commutator 358 Subgroup, normal 16 Subgroup, one-parameter 85 Subgroup, open and closed 33—34 62 Subgroup, proper 4 Subgroup, pure 447 Subnet 14 Sufficiently many 343 Sufficiently many characters 345 Sufficiently many representations 343 Sum of Hilbert spaces 468 Sum of linear spaces 452 Sum of operators 468 Support of a measure 124 Suskevic kernel 101 Swierczkowski, S. 229 Symmetric difference 2 Symmetric group 8 Symmetric matrix 7 Symmetric set 19 Sz.-Nagy, B. 214 375 Szele, T. 27 t 3 T, automorphism group of 433 T, character group is Z 366 T, continuous automorphisms of 369 T, Haar measure on 199 Tarski, A. 220 Thoele, F. 481 Thoma, E. 103 348 Topological automorphism 426 208 Topological field 112 Topological group 16 Topological group, always 83 Topological group, automorphism group of 426—429 Topological group, compactly generated 35 Topological group, discrete 24 Topological group, free 72 Topological group, homomorphism groups of 374 Topological group, independence of axioms 25 Topological group, monothetic 85 Topological group, normal 16 Topological group, ordered 24 Topological group, quotient 40 Topological group, real-character 390 Topological group, self-dual 422 Topological group, solenoidal 85 Topological group, unimodular 196 Topological linear space 453 Topological linear space with only one linear functional 371—373 Topological linear space, locally convex 453 Topological ring 112 Topological semigroup 98 233 Topologically isomorphic 41 Topology, 360 Topology, Gelfand 478 Topology, norm 454 Topology, P- 361 Topology, stronger 9 Topology, weak 458 Topology, weak- 458 Topology, weaker 9 Topology, Weil 229 Torsion group 439 Torsion group, compact characterized 406 Torsion rank 444 Torsion-free group 439 Torsion-free group, compact characterized 406 Torsion-free group, divisible characterized 421 Total variation of a measure 169 Totally bounded metric space 13 Totally disconnected group, small subgroups of 62 Totally disconnected space 11 Toyama, H. 214 Trace of a matrix 7 Transform, Fourier 360 478 Transform, Fourier — Stieltjes 360 Transformation 2 Transitive set of mappings 8 Translate of a function 184 Translation 4 Translation of functions, continuity of 285 305 Transpose of a matrix 7 Triangle inequality 453 Two-sided ideal in a semigroup 100 Two-sided ideal of an algebra 469 Two-sided invariant functional 184 Two-sided invariant mean 230 (see also “Invariant means”) Two-sided invariant pseudo-metric 67 Uniform nearness 20 Uniform norm 119 230 Uniform structures 21 Uniform structures, equivalent 21 Uniform structures, examples 28 Uniformly continuous mapping 21 Unimodular group 196 Unimodular group, compact 196 Unimodular group, equivalent uniform structures 278 Uniqueness of T in duality theorem 424 Unit ball 453 Unit, approximate 303 Unit, relative to I 474—475 Unitary group 7 (see also “ Unitary group, special 7 (see also “ Unitary matrix 7 Unitary operator 467 Unitary representations, continuity equivalences 346 Unitary representations, no finite-dimensional 348 Upper semicontinuous function 121 Urbanik, K. 229 Variation of a measure 169 Vaughan, H.E. 261 Vector space 451—452 Vector, cyclic 315 Vilenkin, N.Ya. 52 60 82 106 375 376 399 423 426 Vitali, G. 283 Volterra, V. 282 Waerden, B. L. van der l Wallace, A.D. 106 Weak direct product of groups 6 Weak direct product of groups, character group of 364—365 Weak topology 458 Weak- 458 Weaker topology 9 Weakly continuous representation 335 Weakly measurable representation 335 Weierstrass, K. 281 282 Weierstrass’s approximation theorem 281—282 Weight function 144 Weil topology 229 Weil, A. 1 32 59 60 83 106 134 135 214 229 283 311 353 354 355 375 398 399 Wendel, J. G. 311 Weyl, H. 213 214 282 283 311 334 353 354 375 Wiener — Hopf equation 282 Wiener, N. 282 375 Wigner, E.P. 26 349 353 Word 8 Yosida, K. 375 Young, W. H. 150 Zero of a semigroup 257 Zippin, L. 32 51 66 76 83 106 398 Zuckerman, H.S. 282 283 312 354 370 435 439 Zygmund, A. 1 282
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