TY  - BOOK
AU  - Edwards, R. E.
TI  - Fourier series: a modern introduction
SN  - 1461381584
U1  - 515.2433 
PY  - 1982///
CY  - New York
PB  - Springer
KW  - Mathematics.
KW  - Topological groups
N1  - 11 Spans of Translates. Closed Ideals. Closed Subalgebras. Banach Algebras --
11.1 Closed Invariant Subspaces and Closed Ideals --
11.2 The Structure of Closed Ideals and Related Topics --
11.3 Closed Subalgebras --
11.4 Banach Algebras and Their Applications --
Exercises --
12 Distributions and Measures --
12.1 Concerning C? --
12.2 Definition and Examples of Distributions and Measures --
12.3 Convergence of Distributions --
12.4 Differentiation of Distributions --
12.5 Fourier Coefficients and Fourier Series of Distributions --
12.6 Convolutions of Distributions --
12.7 More about M and Lp --
12.8 Hilbert's Distribution and Conjugate Series --
12.9 The Theorem of Marcel Riesz --
12.10 Mean Convergence of Fourier Series in LP (1 <p <?) --
12.11 Pseudomeasures and Their Applications --
12.12 Capacities and Beurling's Problem --
12.13 The Dual Form of Bochner's Theorem --
Exercises --
13 Interpolation Theorems --
13.1 Measure Spaces --
13.2 Operators of Type (p, q) --
13.3 The Three Lines Theorem --
13.4 The Riesz-Thorin Theorem --
13.5 The Theorem of Hausdorff-Young --
13.6 An Inequality of W.H. Young --
13.7 Operators of Weak Type --
13.8 The Marcinkiewicz Interpolation Theorem --
13.9 Application to Conjugate Functions --
13.10 Concerning?*f and s*f --
13.11 Theorems of Hardy and Littlewood, Marcinkiewicz and Zygmund --
Exercises --
14 Changing Signs of Fourier Coefficients --
14.1 Harmonic Analysis on the Cantor Group --
14.2 Rademacher Series Convergent in L2 --
14.3 Applications to Fourier Series --
14.4 Comments on the Hausdorff-Young Theorem and Its Dual --
14.5 A Look at Some Dual Results and Generalizations --
Exercises --
15 Lacunary Fourier Series --
15.1 Introduction of Sidon Sets --
15.2 Construction and Examples of Sidon Sets --
15.3 Further Inequalities Involving Sidon Sets --
15.4 Counterexamples concerning the Parseval Formula and Hausdorff-Young Inequalities --
15.5 Sets of Type (p, q) and of Type?(p) --
15.6 Pointwise Convergence and Related Matters --
15.7 Dual Aspects: Helson Sets --
15. 8 Other Species of Lacunarity --
Exercises --
16 Multipliers --
16.1 Preliminaries --
16.2 Operators Commuting with Translations and Convolutions; m-operators --
16.3 Representation Theorems for m-operators --
16.4 Multipliers of Type (LP, Lq) --
16.15 A Theorem of Kaczmarz --
Stein --
16.6 Banach Algebras Applied to Multipliers --
16.7 Further Developments --
16.8 Direct Sum Decompositions and Idempotent Multipliers --
16.9 Absolute Multipliers --
16.10 Multipliers of Weak Type (p, p) --
ER  -