Convolution Operators and Factorization of Almost Periodic Matrix Functions
Published on 23. October 2012
Book
Paperback/Softback
XI, 462 pages
978-3-0348-9457-9 (ISBN)
Description
Many problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a half-line can be studied by having recourse to the methods and results of the theory of Toeplitz and Wiener-Hopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm theory of Toeplitz and Wiener-Hopf operators with continuous and piecewise continuous (matrix) symbols is well presented in a series of classical and recent monographs. Symbols beyond piecewise continuous symbols have discontinuities of oscillating type. Such symbols emerge very naturally. For example, difference operators are nothing but convolution operators with almost periodic symbols: the operator defined by (A
More details
Series
Edition
Softcover reprint of the original 1st ed. 2002
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XI, 462 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 26 mm
Weight
721 gr
ISBN-13
978-3-0348-9457-9 (9783034894579)
DOI
10.1007/978-3-0348-8152-4
Schweitzer Classification
Other editions
Additional editions
Albrecht Böttcher | Yuri I. Karlovich | Ilya M. Spitkovsky
Convolution Operators and Factorization of Almost Periodic Matrix Functions
Book
02/2002
Birkhäuser
€106.99
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Content
1 Convolution Operators and Their Symbols.- 2 Introduction to Scalar Wiener-Hopf Operators.- 3 Scalar Wiener-Hopf Operators with SAP Symbols.- 4 Some Phenomena Caused by SAP Symbols.- 5 Introduction to Matrix Wiener-Hopf Operators.- 6 Factorization of Matrix Functions.- 7 Bohr Compactification.- 8 Existence and Uniqueness ofAPFactorization.- 9 Matrix Wiener-Hopf Operators withAPWSymbols.- 10 Matrix Wiener-Hopf Operators withSAPWSymbols.- 11 Left Versus Right Wiener-Hopf Factorization.- 12 Corona Theorems.- 13 The Portuguese Transformation.- 14 Some Concrete Factorizations.- 15 Scalar Trinomials.- 16 Toeplitz Operators.- 17 Zero-Order Pseudodifferential Operators.- 18 Toeplitz Operators with SAP Symbols on Hardy Spaces.- 19 Wiener-Hopf Operators with SAP Symbols on Lebesgue Spaces.- 20 Hankel Operators on Besicovitch Spaces.- 21 Generalized AP Factorization.- 22 Canonical Wiener-Hopf Factorization via Corona Problems.- 23 Canonical APW Factorization via Corona Problems.