References
N. I. Achiezer, The continuous analogues of some theorems on Toeplitz matrices (Russian). Ukrainian Math. J.16, 445–462 (1964).
E. Basor, A localization theorem for Toeplitz determinants. Indiana Univ. Math. J.28, 975–983 (1979).
E. Basor andH. Widom, Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols. J. Funct. Anal.50, 387–413 (1983).
A. Böttcher, Toeplitz determinants with piecewise continuous generating function. Z. Analysis Anwendungen1, 23–39 (1982).
A. Böttcher, Wiener-Hopf determinants with rational symbols. Math. Nachr.144, 39–64 (1989).
A. Böttcher andB. Silbermann, Wiener-Hopf determinants with symbols having zeros of analytical type. In: Seminar Analysis 1982/83 (Karl-Weierstraß-Institut Berlin), 224–243, Berlin 1983.
A.Böttcher and B.Silbermann, Analysis of Toeplitz Operators. Berlin 1989 and Berlin-Heidelberg-New York 1990.
A.Böttcher, B.Silbermann and H.Widom, A continuous analogue of the Fisher-Hartwig conjecture for piecewise continuous symbols. J. Funct. Anal., to appear.
M. E. Fisher andR. E. Hartwig, Toeplitz determinants—some applications, theorems and conjectures. Adv. Chem. Phys.15, 333–335 (1968).
I.Gohberg and I. A.Feldmann, Convolution Equations and Projection Methods for Their Solution. Amer. Math. Soc. Transl. of Math. Monographs, Vol.41, Providence, R. I., 1977.
I.Gohberg and M. G.Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space. Amer. Math. Soc. Transl, of Math. Monographs, Vol.18, Providence, R. I., 1969.
I. I. Hirschman, Jr., On a formula of Kac and Achiezer. J. Math. Mech.16, 167–196 (1966).
M. Kac, Toeplitz matrices, translation kernels, and a related problem in a probability theory. Duke Math. J.21, 501–509 (1954).
B. Simon, Notes on infinite determinants of Hilbert space operators. Adv. in Math.24, 244–273 (1977).
H. Widom, Asymptotic behavior of block Toeplitz matrices and determinants II. Adv. in Math.21, 1–29 (1976).
H. Widom, On Wiener-Hopf determinants. Oper. Theory: Adv. Appl.41, 519–543 (1989).
Author information
Authors and Affiliations
Additional information
Research supported by the Alfried Krupp Förderpreis für junge Hochschullehrer of the Krupp Foundation.
Research supported by National Science Foundation grant DMS-9216103.
Rights and permissions
About this article
Cite this article
Böttcher, A., Silbermann, B. & Widom, H. Determinants of truncated Wiener-Hopf operators with Hilbert-Schmidt kernels and piecewise continuous symbols. Arch. Math 63, 60–71 (1994). https://doi.org/10.1007/BF01196300
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01196300