Norms of Inverses, Spectra, and Pseudospectra of Large Truncated Wiener-Hopf Operators and

作者: B. Silbermann , S. M. Grudsky , A. Bottcher , Toeplitz Matrices

DOI:

关键词: Uniform boundednessMatrix functionMathematicsAlgebraOperator (computer programming)Toeplitz matrixLimit (mathematics)

摘要: This paper is concerned with Wiener-Hopf integral operators on Lp and Toeplitz (or matrices) lp. The symbols of the op- erators are assumed to be continuous matrix functions. It well known that invertibility operator itself its associated imply all suciently large truncations uniform boundedness norms their inverses. Quantitative statements, such as results limit inverses, can proved in case p = 2 by means C-algebra techniques. In this we replace methods more direct arguments determine inverses thus also pseudospectra general p.

参考文章(28)
Satish C. Reddy, Pseudospectra of Wiener-Hopf Integral Operators and Constant-Coefficient Differential Operators Journal of Integral Equations and Applications. ,vol. 5, pp. 369- 403 ,(1993) , 10.1216/JIEA/1181075761
H. J. Landau, Loss in unstable resonators Journal of the Optical Society of America. ,vol. 66, pp. 525- 529 ,(1976) , 10.1364/JOSA.66.000525
Estelle L. Basor, Kent E. Morrison, The Fisher-Hartwig conjecture and Toeplitz eigenvalues Linear Algebra and its Applications. ,vol. 202, pp. 129- 142 ,(1994) , 10.1016/0024-3795(94)90187-2
Albrecht Böttcher, Bernd Silbermann, The finite section method for TOEPLITZ operators on the quarter-plane with piecewise continuous symbols Mathematische Nachrichten. ,vol. 110, pp. 279- 291 ,(1983) , 10.1002/MANA.19831100120
Bernd Silbermann, On the limiting set of singular values of Toeplitz matrices Linear Algebra and its Applications. ,vol. 182, pp. 35- 43 ,(1993) , 10.1016/0024-3795(93)90490-F
Bernd Silbermann, Lokale Theorie des Reduktionsverfahrens für Toeplitzoperatoren Mathematische Nachrichten. ,vol. 104, pp. 137- 146 ,(1981) , 10.1002/MANA.19811040111
K. Michael Day, Measures associated with Toeplitz matrices generated by the Laurent expansion of rational functions Transactions of the American Mathematical Society. ,vol. 209, pp. 175- 183 ,(1975) , 10.1090/S0002-9947-1975-0383018-7
Evgenij E. Tyrtyshnikov, A unifying approach to some old and new theorems on distribution and clustering Linear Algebra and its Applications. ,vol. 232, pp. 1- 43 ,(1996) , 10.1016/0024-3795(94)00025-5
Bernd Silbermann, Siegfried Prössdorf, Numerical Analysis for Integral and Related Operator Equations ,(1991)
K. Michael Day, Toeplitz matrices generated by the Laurent series expansion of an arbitrary rational function Transactions of the American Mathematical Society. ,vol. 206, pp. 224- 245 ,(1975) , 10.1090/S0002-9947-1975-0379803-8