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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
Biographie de l'auteur
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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An introduction to nonharmonic Fourier series, Volume 93 (Pure and Applied Mathematics)
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Academic Press, 1980
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ISBN 13 : 9780127728506
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An Introduction to Nonharmonic Fourier Series, Volume 93 (Pure and Applied Mathematics)
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Introduction to Nonharmonic Fourier Series (Pure & Applied Mathematics S.)
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An introduction to nonharmonic Fourier series, Volume 93 (Pure and Applied Mathematics)
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Academic Press, 1980
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ISBN 13 : 9780127728506
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An introduction to nonharmonic Fourier series / Robert M. Young
Edité par
New York : Academic Press, 1980
ISBN 10 : 0127728503
ISBN 13 : 9780127728506
Ancien ou d'occasion
Couverture rigide
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1st edition. Fine copy in the original gilt-blocked cloth. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; 257 pp. Contents; Chapter 1. Bases in Banach Spaces; 1 Schauder Bases; 2 Schauder's Basis for C[a,b]; 3 Orthonormal Bases in Hilbert Space; 4 The Reproducing Kernel; 5 Complete Sequences; 6 The Coefficient Functionals; 7 Duality; 8 Reisz Bases; 9 The Stability of Bases in Banach Spaces; 10 The Stability of Orthonormal Bases in Hilbert Space; Chapter 2. Entire Functions of Exponential Type; Part One. The Classical Factorization Theorems; 1 Weierstrass's Factorization Theorem; 2 Jensen's Formula. 3 Functions of Finite Order4 Estimates for Canonical Products; 5 Hadamard's Factorization Theorem; Part Two. Restrictions along a Line; 1 The "Phragmén-Lindelöf" Method; 2 Carleman's Formula; 3 Integrability on a Line; 4 The Paley-Wiener Theorem; 5 The Paley-Wiener Space; Chapter 3. The Completeness of Sets of Complex Exponentials; 1 The Trigonometric System; 2 Exponentials Close to the Trigonometric System; 3 A Counterexample; 4 Some Intrinsic Properties of Sets of Complex Exponentials; 5 Stability; 6 Density and the Completeness Radius; Chapter 4. Interpolation and Bases in Hilbert Space. 1 Moment Sequences in Hilbert Space2 Bessel Sequences and Riesz-Fischer Sequences; 3 Applications to Systems of Complex Exponentials; 4 The Moment Space and Its Relation to Equivalent Sequences; 5 Interpolation in the Paley-Wiener Space: Functions of Sine Type; 6 Interpolation in the Paley-Wiener Space: Stability; 7 The Theory of Frames; 8 The Stability of Nonharmonic Fourier Series; 9 Pointwise Convergence; Notes and Comments; References; List of Special Symbols; Author Index; Subject Index. Subjects; Fourier series. Pre-Calculus. Infinity. Essays. Mathematics. 1 Kg. N° de réf. du vendeur 397225
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An introduction to nonharmonic Fourier series / Robert M. Young
Edité par
New York : Academic Press, 1980
ISBN 10 : 0127728503
ISBN 13 : 9780127728506
Ancien ou d'occasion
Couverture rigide
Edition originale
Vendeur : MW Books, New York, NY, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
1st edition. Fine copy in the original gilt-blocked cloth. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; 257 pp. Contents; Chapter 1. Bases in Banach Spaces; 1 Schauder Bases; 2 Schauder's Basis for C[a,b]; 3 Orthonormal Bases in Hilbert Space; 4 The Reproducing Kernel; 5 Complete Sequences; 6 The Coefficient Functionals; 7 Duality; 8 Reisz Bases; 9 The Stability of Bases in Banach Spaces; 10 The Stability of Orthonormal Bases in Hilbert Space; Chapter 2. Entire Functions of Exponential Type; Part One. The Classical Factorization Theorems; 1 Weierstrass's Factorization Theorem; 2 Jensen's Formula. 3 Functions of Finite Order4 Estimates for Canonical Products; 5 Hadamard's Factorization Theorem; Part Two. Restrictions along a Line; 1 The "Phragmén-Lindelöf" Method; 2 Carleman's Formula; 3 Integrability on a Line; 4 The Paley-Wiener Theorem; 5 The Paley-Wiener Space; Chapter 3. The Completeness of Sets of Complex Exponentials; 1 The Trigonometric System; 2 Exponentials Close to the Trigonometric System; 3 A Counterexample; 4 Some Intrinsic Properties of Sets of Complex Exponentials; 5 Stability; 6 Density and the Completeness Radius; Chapter 4. Interpolation and Bases in Hilbert Space. 1 Moment Sequences in Hilbert Space2 Bessel Sequences and Riesz-Fischer Sequences; 3 Applications to Systems of Complex Exponentials; 4 The Moment Space and Its Relation to Equivalent Sequences; 5 Interpolation in the Paley-Wiener Space: Functions of Sine Type; 6 Interpolation in the Paley-Wiener Space: Stability; 7 The Theory of Frames; 8 The Stability of Nonharmonic Fourier Series; 9 Pointwise Convergence; Notes and Comments; References; List of Special Symbols; Author Index; Subject Index. Subjects; Fourier series. Pre-Calculus. Infinity. Essays. Mathematics. 1 Kg. N° de réf. du vendeur 397225
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