Document Zbl 0499.47017

An abstract version of a limit theorem of Szegoe. (English) Zbl 0499.47017

J. Funct. Anal. 43, 294-312 (1981).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0499.47017

MSC:

47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B35	Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A68	Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47Gxx	Integral, integro-differential, and pseudodifferential operators
45P05	Integral operators

Keywords:

trace class operators; regular factorizations; Fredholm integral operators; Wiener-Hopf operators; maximal chain of orthogonal projections; invertible left factorization; Hilbert-Schmidt; growth of the determinant of the truncates of a Toeplitz matrix; continuous translation kernel

Citations:

Zbl 0048.042; Zbl 0056.102; Zbl 0154.372

Cite Review PDF

Full Text: DOI

References:

[1]	Achiezer, N. I., Amer. Math. Soc. Transl., 50, 295-316 (1966), (2) · Zbl 0178.48201
[2]	Basor, E.; Helton, J. W., A new proof of the Szegö limit theorem and new results for Toeplitz operators with discontinuous symbol, J. Operator Theory, 3, 23-40 (1980) · Zbl 0439.47023
[3]	Devinatz, A., On Wiener-Hopf operators, (Gelbaum, B. R., Proceedings Irvine Conference on Functional Analysis (1967), Thompson: Thompson Washington, D.C), 81-118 · Zbl 0221.47025
[4]	Dym, H., Trace formulas for a class of Toeplitz-like operators, Israel J. Math., 27, 21-48 (1977) · Zbl 0379.47019
[5]	Dym, H., Trace formulas for a class of Toeplitz-like operators, II, J. Funct. Anal., 28, 33-57 (1978) · Zbl 0449.47023
[6]	Dym, H., Trace formulas for pair operators, Integral Equations Operator Theory, 1, 152-175 (1978) · Zbl 0393.47033
[7]	Dym, H., Trace formulas for blocks of Toeplitz-like operators, J. Func. Anal., 31, 69-100 (1979) · Zbl 0418.47014
[8]	Dym, H.; Gohberg, I., On an extension problem, generalized Fourier analysis, and an entropy formula, Integral Equations Operator Theory, 3, 143-215 (1980) · Zbl 0481.42013
[9]	Gohberg, I. C.; Krein, M. G., Introduction to the Theory of Linear Nonselfadjoint Operators, (Trans. Math. Monographs, Vol. 18 (1969), Amer. Math. Soc: Amer. Math. Soc Providence, R.I) · Zbl 0181.13504
[10]	Gohberg, I. C.; Krein, M. G., Theory and Applications of Volterra Operators in Hilbert Space, (Trans. Math. Monographs, Vol. 24 (1970), Amer. Math. Soc: Amer. Math. Soc Providence, R.I) · Zbl 0194.43804
[11]	Gohberg, I. C.; Feldman, I. A., Convolution Equations and Projection Methods for their Solutions, (Trans. Math. Monographs, Vol. 41 (1974), Amer. Math. Soc: Amer. Math. Soc Providence, R.I) · Zbl 0278.45008
[12]	Hirschman, I. I., On a formula of Kac and Achiezer, J. Math. Mech., 16, 167-196 (1966) · Zbl 0154.37203
[13]	Hirschman, I. I., Recent developments in the theory of finite Toeplitz operators, (Ney, P., Advances in Probability, Vol. 1 (1971), Dekker: Dekker New York), 103-167 · Zbl 0301.47030
[14]	Kac, M., Toeplitz matrices, translation kernels and a related problem in probability theory, Duke Math. J., 21, 501-509 (1954) · Zbl 0056.10201
[15]	Mikaelian, L. V., On the multidimensional continual analogue of a theorem of G. Szegö, Izv. Akad. Nauk. Armian SSR Ser. Mat., 11, 275-286 (1976) · Zbl 0366.45006
[16]	Szegö, G., On certain Hermitian forms associated with the Fourier series of a positive function, (Commun. du Séminaire Math. de l’Univ. de Lund, Festshrift Marcel Riesz. Commun. du Séminaire Math. de l’Univ. de Lund, Festshrift Marcel Riesz, Lund (1952)), 228-238 · Zbl 0048.04203
[17]	Widom, H., Asymptotic behavior of block Toeplitz matrices and determinants, Adv. in Math., 13, 284-322 (1974) · Zbl 0281.47018
[18]	Widom, H., On the limit of block Toeplitz determinants, (Proc. Amer. Math. Soc., 50 (1975)), 167-173 · Zbl 0312.47027
[19]	Widom, H., Asymptotic behavior of block Toeplitz matrices and determinants, II, Adv. in Math., 21, 1-29 (1976) · Zbl 0344.47016

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.