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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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Dieudonne, J. 9 25 57 Difference space 452 DIMENSION 15 Dimension of a Hilbert space 465 Direct product of groups 6 Direct product of topological groups 52 Direct product, character group of 362—365 Direct product, local 56—57 Direct product, weak 6 Direct sum of Hilbert spaces 468 Direct sum of linear spaces 452 Directs (directed set) 14 Dirichlet, P. G. L. 281 Discontinuous measure, purely 269 Discrete group 24 Discrete group has compact character group 362 Discrete group, Haar measure on 198 Divisible group 440 Divisible group, characterized 444 Divisible group, imbeddings in 445—447 Divisible group, torsion-free characterized 421 Dixmier, J. 245 393 398 399 Dominated Convergence Theorem 181—182 Dual group 355 (see “Character group”) Duality theorem 378 Duality theorem, uniqueness of T 424 Dunford, N. 149 166 Eckmann, B. 425 Edwards, R.E. 135 Empty set 2 Equidistributions 432 437 Equivalent representations 314 Equivalent uniform structures 21 Erdos, P. 64 Essentially bounded functions 141 Exponential of a matrix 29 Extensibility of characters 380 Extensibility of real characters 391 Extensible positive functional 317 Extensions of Haar measure 216 Extensions of measure spaces 216 Extreme point 459 Extreme subset 459 F. Riesz’s representation theorem 129 F. Riesz’s representation theorem for Hilbert spaces 464 Factor 6 Field of scalars 452 Finite cyclic groups 5 Finite intersection property 2 Finite-dimensional representation, direct sum of irreducibles 333—334 Finite-dimensional representation, no unitary 348—351 Finitely additive measures 118 Finitely additive measures, invariant 242—245 Finitely generated group 449 Finitely generated group, characterized 451 First category 456 First isomorphism theorem for groups 5 First isomorphism theorem for topological groups 44 Folner, E. 245 375 Fourier transform 360 478 Fourier — Stieltjes transform 360 Free Abelian group 8 Free group 8 Free topological group 72 Freudenthal, H. 32 49 51 52 60 355 375 393 399 Frobenius, G. 213 375 Fubini’s Theorem 153—156 Fubini’s theorem for complex measures 183 Fuchs, L. 381 425 Functional, bilinear 453 Functional, bounded bilinear 468 Functional, conjugate-linear 452 Functional, linear 452 Functional, multiplicative linear 474 Functional, nonnegative 461 Functional, positive 316 Functional, relatively bounded 461 Functional, strictly positive 461 Functional, total variation of 168 Fundamental theorem of Abelian groups 451 Gelbaum, B. 104 Gelfand topology 478 Gelfand — Mazur theorem 473 Gelfand — Naimark theorem 481 Gelfand — Raikov theorem 343 Gelfand, I.M. 282 311 334 353 354 375 Gelfand’s theorem 478 General linear group 7 (see also “ Generator of monothetic group 105 407 415 Glicksberg, I. 135 Godement, R. 309 311 332 334 353 354 398 Grabar’, L. 80 Graev, M.I. 47 50 60 74 79 82 83 Group of bounded order 439 Group, (abelian group in Appendix A) 439 (see also “Topological group”) Group, bounded order characterized 449 Group, divisible 440 Group, finite cyclic 5 Group, finitely generated 449 Group, free 8 Group, free abelian 8 Group, linear 7 Group, p-primary 439 Group, permutation 8 Group, reduced 440 Group, symmetric 8 Group, topological see “Topological group” Group, torsion 439 Group, torsion-free 439 Gurevic, A. 354 Haar integral (left) 184—194 (see also “Haar measure”) Haar integral, examples of 198 209 Haar integral, existence and uniqueness of 185—193 Haar integral, right 195 Haar measure (left) 194 Haar measure and Baire sets 280 Haar measure, examples of 198 209 Haar measure, extensions of 216 Haar measure, right 195 Haar measure, uniqueness of 193—194 Haar, A. 1 32 214 375 Hahn — Banach theorem 454—455 Hall, M. Jr. 26 Halmos, P.R. 229 261 280 398 415 425 Hamel, G. 425 Hardy, G.H. 149 Harrison, D. K. 425 Hartman, S. 68 393 395 398 Helson, H. 311 Hensel, K. 117 Hermitian element 313 Hermitian matrix 7 Hermitian operator 467 Hermitian operator, spectral theorem for 491 Hermitian operator, spectrum is real 484 Hewitt, E. 105 135 184 261 282 283 312 354 370 375 397 435 439 Hilbert space 464 Hilbert space, dimension of 465 Hilbert space, direct sum of 468 Hofmann, K.H. 64 439 Holder’s Inequality 137 Homogeneous function 452 Homogeneous space 9 Homogeneous space, quotient spaces 37 Homomorphism group 374 Homomorphism, adjoint 392 Homomorphism, algebra 470 Hopf, H. 47 Hulanicki, A. 79 106 395 425 Hurwitz, A. 213 Ideal in a semigroup 100 Ideal of an algebra 469 Ideal, regular 475 Ideal, regular left 474 Idempotent 99 Independent subset of a group 441—442 Independent subset of a group, pure 448 Infinity, conventions regarding 119 Inner automorphisms 4 Inner automorphisms, topological group of 439 Inner product 464 Inner product for 139 Inner product in 3 Inner product space 464 Integral, Lebesgue 119 Invariant finitely additive measures 242—245 Invariant linear functional 184 Invariant means 230 Invariant means for Invariant means for 240 Invariant means, groups not admitting 236 Invariant means, uniqueness of 241 Invariant pseudo-metric 67 Invariant set function 185 Invariant subspace (under a representation) 313 Inverse mapping system 55 Inverses, form open set 473 Inversion invariant functional 184 Inversion invariant set function 185 Inversion mapping 4 Irreducible representation 323 Irreducible representation, equivalent properties 324 Irreducible set of operators 323 Isiwata, T. 399 Isometry, linear 464 Isomorphism theorems 5 44—45 Ivanovskii, L.N. 106 Iwamura, T. 375 Iwasawa, K. 26 439 Jamison, R. E. 132 Jones, F. B. 79 Kakutani — Oxtoby extension of Haar measure 216 Kakutani, S. 78 81 83 134 214 215 229 280 396 398 399 425 439 Kalisch, G.K. 104 Kampen, E.R. van 32 51 67 104 106 354 375 397 398 Kaplan, S. 399 Kaplansky, I. 398 425 Kasuga, T. 58 Kawada, Y. 26l Keiner, H. 259 Kelley, J.L. 1 460 Kemperman, J.H.B. 229 Kernel of a semigroup 101 Kertesz, A. 27 Kesten, H. 245 Klee, V. L. 371 Kneser, M. 229 Kodaira, K. 83 280 Konig’s theorem 217 Koosis, P. 354 Krein — Milman theorem 460 Krein — Milman theorem, applied 330 Krein, M. G. 282 Kristensen, L. 77 Kronecker approximation theorems 431 435 436 Kronecker’s delta function 3 Krull, W. 425 Kuros, A. G. 26 Kuz’minov, V. 106 Lattice 461 Lebesgue integral 119 Lebesgue — Radon — Nikodym theorem 144 Lebesgue, H. 150 283 Lebesgue’s theorem on dominated convergence 181—182 Left cancellation law 98—99 Left Haar integral 184—194 (see also “Haar integral”) Left Haar measure 194 (see also “Haar measure”) Left ideal in a semigroup 100 Left ideal of an algebra 469 Left ideal, regular 474 Left invariant functional 184 Left invariant mean 230 (see also “Invariant means”) Left invariant pseudo-metric 67 Left invariant set function 185 Left quasi-inverse 471 Left translate of a function 184 Left translation 4 Left uniform structure 21 Left unit relative to I 474—475 Lehmer, D.H. 282 Leja, F. 31 67 Length of reduced word 8 Leptin, H. 399 Levi, F. 51 Lindelof property 11 Linear function 452 Linear function, bounded 454 Linear function, norm of 454 Linear functional(s) 452 Linear functional(s), bounded 454 Linear functional(s), infinite product of 159 Linear functional(s), inversion invariant 184 Linear functional(s), left invariant 184 Linear functional(s), multiplicative 474 Linear functional(s), nonnegative 461 Linear functional(s), nonnegative on 120 Linear functional(s), norm of 454 Linear functional(s), positive 316 Linear functional(s), product of 152 159 Linear functional(s), relatively bounded 461 Linear functional(s), strictly positive 461 Linear functional(s), two-sided invariant 184 Linear functional(s), unbounded on 167 Linear groups 7 29—31 Linear groups, topologies in 24 Linear isometry 464 Linear space(s) 451—452 Linear space(s), Banach 455 Linear space(s), conjugate of 457 Linear space(s), direct sum of 452 Linear space(s), Hilbert 464 Linear space(s), inner product 464 Linear space(s), locally convex 453 Linear space(s), normed 453 Linear space(s), topological 453 Linear subspace 452 Linear transformation 452 Littlewood, J.E. 149 Local direct product 56—57 Local direct product, character group of 373 Local direct product, self-dual 422 Locally 124 Locally 124 Locally 124 Locally almost everywhere 124 Locally arcwise connected space 12 Locally bounded group 215 Locally compact groups, normality of 76 Locally compact space 11 Locally connected compact Abelian groups 399 Locally connected space 11 Locally convex space 453 Locally countably compact space 11 Locally Euclidean space 13 Locally Euclidean space, linear groups are 29—31 Locally finite 13 Locally null function 124 Locally null nonnull sets 127 228 Locally null set 124 Loomis, L.H. 32 135 215 311 353
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