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

  • ID: 1756888
  • Book
  • 234 Pages
  • Elsevier Science and Technology
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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.
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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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Young, Robert M.
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.
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