Fourier Analysis on GroupsJohn Wiley & Sons, 16 janv. 1991 - 304 pages 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. |
Table des matières
CHAPTER | 1 |
CHAPTER 5 | 97 |
5 | 112 |
CHAPTER 9 | 129 |
CHAPTER 6 | 131 |
CHAPTER 7 | 157 |
Appendices | 203 |
Topology | 247 |
| 271 | |
List of Special Symbols | 281 |
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Expressions et termes fréquents
abelian group Appendix AR(T Banach algebra Borel function Borel set Cantor set closed ideal closed subgroup compact set compact support completes the proof complex homomorphism continuous converges coset countable dense direct sum disjoint element exists F is analytic F is defined F operates F₁ F₂ fe L¹(G finite Fourier transform Fourier-Stieltjes transform function F G is compact G₁ G₂ Haar measure Hausdorff space Helson set Hence homomorphism implies inequality infinite isomorphism K₁ Kronecker set L¹(G L¹(G₁ L¹(R LCA group G Lemma locally compact metric n₁ norm open set open subgroup polynomial on G proof is complete proof of Theorem proved real number Rudin S-set S₁ sequence shows Sidon set subgroup of G subspace Suppose G T₁ T₂ topology translates trigonometric polynomial V₁ x e G y)dy y₁