An introduction to nonharmonic Fourier series

Robert M. Young0127728503, 9780127728506, 9780080874098

An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook. Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

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Table of contents :
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