Convolution Operators and Factorization of Almost Periodic Matrix Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2002
|
| Schriftenreihe: | Operator Theory: Advances and Applications
131 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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<p)(x) = L: ak"kX. Moreover, a convolution operator on a finite interval is, in a sense, equivalent to a convolution operator on the half-line whose symbol is a 2 x 2 oscillating matrix function: consideration of the convolution operator with the symbol f(x) on the interval (0, A) leads to the convolution operator with the matrix symbol on the half-line (0,00). Notice that eVl(x) is oscillating even if f(x) is continu ous. We finally mention that convolution operators with oscillating symbols have properties that are not shared by operators with continuous or piecewise continu ous symbols |
| Beschreibung: | 1 Online-Ressource (XI, 462 p) |
| ISBN: | 9783034881524 9783034894579 |
| DOI: | 10.1007/978-3-0348-8152-4 |
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| isbn | 9783034881524 9783034894579 |
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| spelling | Böttcher, Albrecht Verfasser aut Convolution Operators and Factorization of Almost Periodic Matrix Functions by Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky Basel Birkhäuser Basel 2002 1 Online-Ressource (XI, 462 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 131 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<p)(x) = L: ak"kX. Moreover, a convolution operator on a finite interval is, in a sense, equivalent to a convolution operator on the half-line whose symbol is a 2 x 2 oscillating matrix function: consideration of the convolution operator with the symbol f(x) on the interval (0, A) leads to the convolution operator with the matrix symbol on the half-line (0,00). Notice that eVl(x) is oscillating even if f(x) is continu ous. We finally mention that convolution operators with oscillating symbols have properties that are not shared by operators with continuous or piecewise continu ous symbols Mathematics Operator theory Operator Theory Mathematik Faltungsoperator (DE-588)4388315-1 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Matrixfunktion (DE-588)4169117-9 gnd rswk-swf Faltungsoperator (DE-588)4388315-1 s Matrixfunktion (DE-588)4169117-9 s Faktorisierung (DE-588)4128927-4 s 1\p DE-604 Karlovich, Yuri I. Sonstige oth Spitkovsky, Ilya M. Sonstige oth https://doi.org/10.1007/978-3-0348-8152-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Böttcher, Albrecht Convolution Operators and Factorization of Almost Periodic Matrix Functions Mathematics Operator theory Operator Theory Mathematik Faltungsoperator (DE-588)4388315-1 gnd Faktorisierung (DE-588)4128927-4 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| subject_GND | (DE-588)4388315-1 (DE-588)4128927-4 (DE-588)4169117-9 |
| title | Convolution Operators and Factorization of Almost Periodic Matrix Functions |
| title_auth | Convolution Operators and Factorization of Almost Periodic Matrix Functions |
| title_exact_search | Convolution Operators and Factorization of Almost Periodic Matrix Functions |
| title_full | Convolution Operators and Factorization of Almost Periodic Matrix Functions by Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky |
| title_fullStr | Convolution Operators and Factorization of Almost Periodic Matrix Functions by Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky |
| title_full_unstemmed | Convolution Operators and Factorization of Almost Periodic Matrix Functions by Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky |
| title_short | Convolution Operators and Factorization of Almost Periodic Matrix Functions |
| title_sort | convolution operators and factorization of almost periodic matrix functions |
| topic | Mathematics Operator theory Operator Theory Mathematik Faltungsoperator (DE-588)4388315-1 gnd Faktorisierung (DE-588)4128927-4 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| topic_facet | Mathematics Operator theory Operator Theory Mathematik Faltungsoperator Faktorisierung Matrixfunktion |
| url | https://doi.org/10.1007/978-3-0348-8152-4 |
| work_keys_str_mv | AT bottcheralbrecht convolutionoperatorsandfactorizationofalmostperiodicmatrixfunctions AT karlovichyurii convolutionoperatorsandfactorizationofalmostperiodicmatrixfunctions AT spitkovskyilyam convolutionoperatorsandfactorizationofalmostperiodicmatrixfunctions |