| Convolution Operators and Factorization of Almost Periodic Matrix Functions 2002 Edition Contributor(s): Böttcher, Albrecht (Author), Karlovich, Yuri I. (Author), Spitkovsky, Ilya M. (Author) |
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ISBN: 3764366729 ISBN-13: 9783764366728 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: February 2002 Annotation: This book is an introduction to convolution operators with matrix-valued almost periodic or semi-almost periodic symbols.The basic tools for the treatment of the operators are Wiener-Hopf factorization and almost periodic factorization. These factorizations are systematically investigated and explicitly constructed for interesting concrete classes of matrix functions. The material covered by the book ranges from classical results through a first comprehensive presentation of the core of the theory of almost periodic factorization up to the latest achievements, such as the construction of factorizations by means of the Portuguese transformation and the solution of corona theorems. The book is addressed to a wide audience in the mathematical and engineering sciences. It is accessible to readers with basic knowledge in functional, real, complex, and harmonic analysis, and it is of interest to everyone who has to deal with the factorization of operators or matrix functions. |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Medical - Mathematics | Probability & Statistics - General |
| Dewey: 515.724 |
| LCCN: 2001052523 |
| Series: Operator Theory: Advances and Applications |
| Physical Information: 1.06" H x 6.14" W x 9.21" (1.86 lbs) 462 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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 |