Bibliographic Details
| Title: |
Around a multivariate Schmidt–Spitzer theorem. |
| Authors: |
Alexandersson, Per1 per@math.su.se, Shapiro, Boris1 shapiro@math.su.se |
| Source: |
Linear Algebra & its Applications. Apr2014, Vol. 446, p356-368. 13p. |
| Subjects: |
Multivariate analysis, Arbitrary constants, Mathematical proofs, Toeplitz matrices, Polynomials |
| Abstract: |
Abstract: Given an arbitrary complex-valued infinite matrix , ; and a positive integer n we introduce a naturally associated polynomial basis of . We discuss some properties of the locus of common zeros of all polynomials in having a given degree m; the latter locus can be interpreted as the spectrum of the -submatrix of formed by its m first rows and by the first columns. We initiate the study of the asymptotic of these spectra when in the case when is a banded Toeplitz matrix. In particular, we present and partially prove a conjectural multivariate analog of the well-known Schmidt–Spitzer theorem which describes the spectral asymptotic for the sequence of principal minors of an arbitrary banded Toeplitz matrix. Finally, we discuss relations between polynomial bases and multivariate orthogonal polynomials. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
