Elsevier S & T

An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93

Young, Robert M.

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Table of contents
  • Cover
  • Contentsvii
  • Preface to the Revised First Editionxi
  • Preface to the First Editionxiii
  • Chapter 1. Bases in Banach Spaces1
  • 1 Schauder Bases1
  • 2 Schauder’s Basis for C[a, b]3
  • 3 Orthonormal Bases in Hilbert Space5
  • 4 The Reproducing Kernel13
  • 5 Complete Sequences16
  • 6 The Coefficient Functionals19
  • 7 Duality22
  • 8 Riesz Bases25
  • 9 The Stability of Bases in Banach Spaces31
  • 10 The Stability of Orthonormal Bases in Hilbert Space35
  • Chapter 2. Entire Functions of Exponential Type45
  • Part one. The Classical Factorization Theorems46
  • 1 Weierstrass’s Factorization Theorem46
  • 2 Jensen’s Formula50
  • 3 Functions of Finite Order53
  • 4 Estimates for Canonical Products59
  • 5 Hadamard’s Factorization Theorem63
  • Part two. Restrictions along a Line68
  • 1 The Phragmén…Lindel¨öfŽ Method68
  • 2 Carleman’s Formula74
  • 3 Integrability on a Line79
  • 4 The Paley–Wiener Theorem85
  • 5 The Paley–Wiener Space90
  • Chapter 3. The Completeness of Sets of Complex Exponentials93
  • 1 The Trigonometric System94
  • 2 Exponentials Close to the Trigonometric System99
  • 3 A Counterexample102
  • 4 Some Intrinsic Properties of Sets of Complex Exponentials106
  • 5 Stability110
  • 6 Density and the Completeness Radius115
  • Chapter 4. Interpolation and Bases in Hilbert Space121
  • 1 Moment Sequences in Hilbert Space122
  • 2 Bessel Sequences and Riesz–Fischer Sequences128
  • 3 Applications to Systems of Complex Exponentials135
  • 4 The Moment Space and Its Relation to Equivalent Sequences139
  • 5 Interpolation in the Paley–Wiener Space: Functions of Sine Type142
  • 6 Interpolation in the Paley–Wiener Space: Stability149
  • 7 The Theory of Frames154
  • 8 The Stability of Nonharmonic Fourier Series160
  • 9 Pointwise Convergence165
  • Notes and Comments171
  • References199
  • List of Special Symbols221
  • Author Index223
  • Subject Index229
Book details
  • Vendor Elsevier S & T
  • SKU 9780127729558
  • ISBN-13 9780080495743
  • Author Young, Robert M.
  • Edition 2nd
  • Category Mathematics
  • Subject Infinity

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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.