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


  • Robert Young, Oberlin College, Ohio, U.S.A.

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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Junior and senior undergraduate and first-year graduate students in mathematics.


Book information

  • Published: May 2001
  • ISBN: 978-0-12-772955-8


From Book News, Inc. The theory of nonharmonic Fourier series is concerned with the completeness and expansion properties of sets of complex exponential functions. This text for graduate students and mathematicians provides an introduction to some of the classical and modern theories within this broad field. Young (mathematics, Oberlin College) discusses such topics as the stability of bases in Banach spaces, estimates for canonical products, and moment sequences in Hilbert space.Book News, Inc.®, Portland, OR

Table of Contents

Bases in Banach Spaces - Schauder Bases; Schauder's Basis for C[a,b]; Orthonormal Bases in Hilbert Space; The Reproducing Kernel; Complete Sequences; The Coefficient Functionals; Duality; Riesz Bases; The Stability of Bases in Banach Spaces; The Stability of Orthonormal Bases in Hilbert SpaceEntire Functions of Exponential TypeThe Classical Factorization Theorems - Weierstrass's Factorization Theorem; Jensen's Formula; Functions of Finite Order; Estimates for Canonical Products; Hadamard's Factorization TheoremRestrictions Along a Line - The "Phragmen-Lindelof" Method; Carleman's Formula; Integrability on a line; The Paley-Wiener Theorem; The Paley-Wiener SpaceThe Completeness of Sets of Complex Exponentials - The Trigonometric System; Exponentials Close to the Trigonometric System; A Counterexample; Some Intrinsic Properties of Sets of Complex ExponentialsStability; Density and the Completeness RadiusInterpolation and Bases in Hilbert Space - Moment Sequences in Hilbert Space; Bessel Sequences and Riesz-Fischer Sequences; Applications to Systems of Complex Exponentials; The Moment Space and Its Relation to Equivalent Sequences; Interpolation in the Paley-Wiener Space: Functions of Sine Type; Interpolation in the Paley-Wiener Space: Stability; The Theory of Frames; The Stability of Nonharmonic Fourier Series; Pointwise Convergence; Notes and Comments; References; List of Special SymbolsIndex