Pseudospectra and singular values of large convolution operators

Journal of Integral Equations and Applications

Volumn 6, Issue 3, 1994, Pages 267-301

  Böttcher, Albrecht ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000820448     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075815     Document Type: Article

References (27)

1. P. M. Anselone and I. H. Sloan, Spectral approximations for Wiener-Hopf operators II, J. Integral Equations Appl. 4 (1992), 465-489.
2. E. Basor and K. E. Morrison, The Fisher-Hartwig conjecture and Toeplitz eigenvalues, Linear and Multilinear Algebra, to appear.
3. A. Böttcher, Analysis lokal sektorieller Matrixfunktionen und geometrische Spektraltheorie von Toeplitzoperatoren, Habilitationsschrift, TU Karl-Marx-Stadt, 1987.
4. A. Böttcher and B. Silbermann, The finite section method for Toeplitz operators on the quarter-plane with piecewise continuous symbols, Math. Nachr. 11 (1983), 279-291.
5. A. Böttcher and B. Silbermann, Toeplitz operators and determinants generated by symbols with one Fisher-Hartwig singularity, Math. Nachr. 127 (1986), 95-124.
6. A. Böttcher and B. Silbermann, Analysis of Toeplitz operators, Springer-Verlag, Berlin, Heidelberg, New York, 1990.
7. A. Böttcher and H. Widom, Two remarks on spectral approximations for Wiener-Hopf operators, J. Integral Equations Appl. 6 (1994), 31-36.
8. A. Brown and P. Halmos, Algebraic properties of Toeplitz operators, J. reine angew. Math. 213 (1963), 89-102.
9. K. M. Day, Measures associated with Toeplitz matrices generated by Laurent expansion of rational functions, Trans. Amer. Math. Soc. 209 (1975), 175-183.
10. J. Dixmier, Les C*-alqèbres et leurs representations, Gauthier-Villars, Paris, 1969.
11. R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972.
12. R. Duduchava, Integral equations with fixed singularities, Teubner, Leipzig, 1979.
13. I. Gohberg and I. A. Feldman, Convolution equations and projection methods for their solution, Amer. Math. Soc., Providence, RI, 1974 (Russian original: Nauka, Moscow, 1971; German translation: Akademie-Verlag, Berlin, 1974).
14. I. Gohberg and N. Ya. Krupnik, On the algebra generated by Toeplitz matrics, Funct. Anal. Appl. 3 (1969), 119-127.
15. R. A. Libby, Asymptotics of determinants and eigenvalue distributions of Toeplitz matrices with certain discontinuous symbols, Ph. D. thesis, University of California, Santa Cruz, 1990.
16. S. V. Parter, On the distribution of the singular values of Toeplitz matrices, Linear Algebra Appl. 80 (1986), 115-130.
17. S. C. Reddy, Pseudospectra of Wiener-Hopf integral operators and constant-coefficient differential operators, J. Integral Equations Appl. 5 (1993), 369-403.
18. L. Reichel and L. N. Trefethen, Eigenvalues and pseudo-eigenvalues of Toeplitz matrices, Linear Algebra Appl. 162 (1992), 153-185.
19. P. Schmidt and F. Spitzer, The Toeplitz matrices of an arbitrary Laurent polynomial, Math. Scand. 8 (1960), 15-38.
20. B. Silbermann, Lokale Theorie des Reduktionsverfahrens für Toeplitz-operatoren, Math. Nachr. 104 (1982), 45-56.
21. B. Silbermann, On the limiting set of singular values of Toeplitz matrices, Linear Algebra Appl. 182 (1993), 35-43.
22. G. Szegö, Beitrăge zur Theorie der Toeplitzschen Formen I, Math. Z. 6 (1920), 167-202.
23. S. R. Treil, The invertibility of a Toeplitz operator does not imply its invert-ibility by the projection method, Sov. Math. Dokl. 35 (1987), 103-107.
24. H. Widom, Toeplitz matrices, Studies in Real and Complex Analysis (I. I. Hirschman, Jr., ed.), MAA Stud. Math. 3 (1965), 179-209.
25. H. Widom, Asymptotic behavior of block Toeplitz matrices and determinants II, Adv. Math. 21 (1976), 1-29.
26. H. Widom, On the singular values of Toeplitz matrices, Z. Anal. Anwendungen 8 (1989), 221-229.
27. H. Widom, Eigenvalue distribution of nonself adjoint Toeplitz matrices and the asymptotics of Toeplitz determinants in the case of nonvanishing index, Oper. Theory Adv. Appl. 48 (1990), 387-421.