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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the limit of block Toeplitz determinants


Author: Harold Widom
Journal: Proc. Amer. Math. Soc. 50 (1975), 167-173
MSC: Primary 47B35
MathSciNet review: 0370254
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Abstract: An asymptotic formula is derived for block Toeplitz determinants which generalizes Szegö's well-known formula for ordinary Toeplitz determinants.


References [Enhancements On Off] (What's this?)

  • [1] I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR 0246142 (39 #7447)
  • [2] J. William Helton and Roger E. Howe, Integral operators: commutators, traces, index and homology, Proceedings of a Conference Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Springer, Berlin, 1973, pp. 141–209. Lecture Notes in Math., Vol. 345. MR 0390829 (52 #11652)
  • [3] J. D. Pincus, On the trace of commutators in the algebra of operators generated by an operator with trace class self-commutator, 1972 (unpublished).
  • [4] Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101 (22 #5903)
  • [5] Harold Widom, Asymptotic behavior of block Toeplitz matrices and determinants, Advances in Math. 13 (1974), 284–322. MR 0409511 (53 #13266a)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0370254-4
PII: S 0002-9939(1975)0370254-4
Article copyright: © Copyright 1975 American Mathematical Society