Asymptotic inverse of Toeplitz matrices with symbol \((1-\cos \theta )^\alpha f_1\), \(\frac{-1}{2} <\alpha \leq\frac12\), and integral kernels

DOI10.1016/j.bulsci.2008.03.001zbMath1191.47046OpenAlexW1977387117MaRDI QIDQ2270132

Abdellatif Seghier, Philippe Rambour

Publication date: 12 March 2010

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2008.03.001

zbMATH Keywords

orthogonal polynomialsingular symbolinversion of Toeplitz matrix

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other special orthogonal polynomials and functions (33C47) Linear difference operators (47B39) Toeplitz, Cauchy, and related matrices (15B05)

Related Items

Entries of the inverses of large positive definite Toeplitz matrices ⋮ Orthogonal polynomials with respect to a class of Fisher-Hartwig symbols and inverse of Toeplitz matrices ⋮ Inversion of Toeplitz matrices whose symbols admit a root of positive rational order for the minimal eigenvalue. ⋮ Minimal eigenvalues of Toeplitz matrices and of products of Toeplitz matrices ⋮ The generalised Dyson circular unitary ensemble: asymptotic distribution of the eigenvalues at the origin of the spectrum ⋮ Factorization of positive functions on the torus: applications to truncated Toeplitz operators

Cites Work

• The constants in the asymptotic formulas by Rambour and Seghier for inverses of Toeplitz matrices
• Formulas for the inverses of Toeplitz matrices with polynomially singular symbols
• Trace theorems of Szegő type in the singular case.
• A class of Toeplitz forms and their application to probability theory
• Random walks with absorbing barriers and Toeplitz forms
• Maximum entropy and the moment problem
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