AN INTRODUCTION TO NON-HARMONIC FOURIER SERIES, REVISED EDITION, 93
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By Robert Young, Oberlin College, Ohio, U.S.A.
Description 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.
Audience
Junior and senior undergraduate and first-year graduate students in mathematics.
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 Space
Entire Functions of Exponential Type
The Classical Factorization Theorems - Weierstrass's Factorization Theorem;
Jensen's Formula; Functions of Finite Order; Estimates for Canonical Products; Hadamard's Factorization Theorem
Restrictions Along a
Line - The "Phragmen-Lindelof" Method; Carleman's Formula; Integrability on a line; The Paley-Wiener Theorem; The Paley-Wiener Space
The Completeness of Sets of Complex Exponentials -
The Trigonometric System; Exponentials Close to the Trigonometric System; A Counterexample;
Some Intrinsic Properties of Sets of Complex Exponentials
Stability; Density and the Completeness Radius
Interpolation 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 Symbols
Index
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