An Introduction to Nonharmonic Fourier Series (Pure and Applied Mathematics (Academic Pr))

Series......Page 1
Title page......Page 2
Date-line......Page 3
Dedication......Page 4
CONTENTS......Page 6
Preface......Page 8
1 Schauder Bases......Page 10
2 Schauder\'s Basis for C[a,b]......Page 12
3 Orthonormal Bases in Hilbert Space......Page 15
4 The Reproducing Kernel......Page 24
5 Complete Sequences......Page 28
6 The Coefficient Functional......Page 31
7 Duality......Page 36
8 Reisz Bases......Page 39
9 The Stability of Bases in Banach Spaces......Page 46
10 The Stability of Orthonormal Bases in Hilbert Space......Page 50
2. Entire Functions of Exponential Type......Page 62
1 Weierstrass\'s Factorization Theorem......Page 63
2 Jensen\'s Formula......Page 68
3 Functions of Finite Order......Page 71
4 Estimates for Canonical Products......Page 78
5 Hadamard\'s Factorization Theorem......Page 83
1 The \\\"Phragmen-Lindelof\\\" Method......Page 89
2 Carleman\'s Formula......Page 96
3 Integrability on a Line......Page 102
4 The Paley-Wiener Theorem......Page 109
5 The Paley-Wiener Space......Page 114
3. The Completeness of Sets of Complex Exponentials......Page 120
1 The Trigonometric System......Page 121
2 Exponentials Close to the Trigonometric System......Page 127
3 A Counterexample......Page 131
4 Some Intrinsic Properties of Sets of Complex Exponentials......Page 135
5 Stability......Page 140
6 Density and the Completeness Radius......Page 146
4. Interpolation and Bases in Hilbert Space......Page 154
1 Moment Sequences in Hilbert Space......Page 155
2 Bessel Sequences and Riesz-Fischer Sequences......Page 162
3 Applications to Systems of Complex Exponentials......Page 171
4 The Moment Space and Its Relation to Equivalent Sequences......Page 176
5 Interpolation in the Paley-Wiener Space: Functions of Sine Type......Page 179
6 Interpolation in the Paley-Wiener Space: Stability......Page 188
7 The Theory of Frames......Page 193
8 The Stability of Nonharmonic Fourier Series......Page 199
9 Pointwise Convergence......Page 206
Notes and Comments......Page 212
References......Page 234
List of Special Symbols......Page 244
Author Index......Page 246
Subject Index......Page 250