Asymptotic Forms of Some Block Toeplitz Determinants
نویسندگان
چکیده
منابع مشابه
Block - Toeplitz Determinants
We evaluate the Geiss-Leclerc-Schröer φ-map for shape modules over the preprojective algebra Λ of type c A1 in terms of matrix minors arising from the block-Toeplitz representation of the loop group SL2(L). Conjecturally these minors are among the cluster variables for coordinate rings of unipotent cells within SL2(L). In so doing we compute the Euler characteristic of any generalized flag vari...
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The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obtained are applied to vector asymptotically wide...
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It is well known that the generating function f ∈ L([−π, π],R) of a class of Hermitian Toeplitz matrices An(f) describes very precisely the spectrum of each matrix of the class [U. Grenader and G. Szegö, Toeplitz Forms and Their Applications, 2nd ed., Chelsea, New York, 1984; E. E. Tyrtyshnikov, Linear Algebra Appl., 232 (1996), pp. 1–43]. In this paper we consider n×n block Toeplitz matrices w...
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We study the asymptotic behaviour of the eigenvalues of Hermitian n × n block Toeplitz matrices An,m, with m ×m Toeplitz blocks. Such matrices are generated by the Fourier coefficients of an integrable bivariate function f , and we study their eigenvalues for large n and m, relating their behaviour to some properties of f as a function; in particular we show that, for any fixed k, the first k e...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1990
ISSN: 0033-068X
DOI: 10.1143/ptp.84.410