Synopses & Reviews
The theory of nonharmonic Fourier series is concerned with the completeness and expansion properties of sets of complex exponential functions. Its origins, which are classical in spirit, lie in the celebrated works of Paley and Wiener (Fourier Transforms in the Complex Domain) and Levinson (Gap and Density Theorems).
This book is an account of both the classical and modern theories and its
underlying theme is the elegant interplay among the various parts of
analysis. Designed primarily for the graduate student or mathematician who
is approaching the subject for the first time, its aim is to provide a unified and self-contained introduction to a rich and multifaceted field, not an
exhaustive account of all that is known.
The new edition brings the original work up to date.
Synopsis
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.
Synopsis
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.
Synopsis
g the subject for the first time, its aim is to provide a unified and self-contained introduction to a rich and multifaceted field, not an
exhaustive account of all that is known.
The new edition brings the original work up to date.
Synopsis
introduction to a rich and multifaceted field, not an
exhaustive account of all that is known.
The new edition brings the original work up to date.
Description
Includes bibliographical references (p. 199-219) and index.
About the Author
Robert Young was born in New York City in 1944. He received his B.A. from Colby College in 1965 and his Ph.D. from the University of Michigan in 1971. He currently teaches at Oberlin College where he holds the James F. Clark Chair in Mathematics. In addition to his work in nonharmonic Fourier series, he is the author of Excursions in Calculus: An Interplay of the Continuous and the Discrete.
Oberlin College, Ohio, U.S.A.
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 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