Fourier Analysis on GroupsJohn Wiley & Sons, 9 set 2011 - 304 pagine In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained. |
Sommario
| 1 | |
Chapter 2 The Structure of Locally Compact Abelian Groups | 35 |
Chapter 3 Idempotent Measures | 59 |
Chapter 4 Homomorphisms of Group Algebras | 77 |
Chapter 5 Measures and Fourier Transforms on Thin Sets | 97 |
Chapter 6 Functions of Fourier Transforms | 131 |
Chapter 7 Closed Ideals in L1 G | 157 |
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abelian group analytic Appendix Banach algebra Borel function Borel set Cantor set closed ideal closed subgroup compact abelian group compact set compact support completes the proof complex homomorphism converges coset countable defined dense direct sum disjoint dual group element exists F operates f₁ fe L¹(G finite Fourier transform Fourier-Stieltjes transforms G is compact G₁ G₂ H²(G Haar measure Hausdorff space Helson set Hence homomorphism implies inequality infinite isomorphism Kronecker set L¹(G L¹(G₁ L¹(R L¹(S L²(G LCA group G Lemma locally compact Math metric n₁ non-negative norm open set open subgroup piecewise affine proof is complete proof of Theorem proved real number Rudin S-set sequence shows Sidon set subgroup of G subspace Suppose G topology translates trigonometric polynomial x e G x₁ xe G y)dy y₁