Toeplitz operators of finite interval type and the table method

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Camara, M. C.¹  Diogo, C.^1,2  Spitkovsky, I. M.^3,4 

[1] Univ Lisbon, Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Dept Math, P-1049001 Lisbon, Portugal

[2] Inst Univ Lisboa, Dept Matemat, P-1649026 Lisbon, Portugal

[3] New York Univ Abu Dhabi, Div Sci & Math, Abu Dhabi, U Arab Emirates

[4] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

关键词: Toeplitz operator';    Riemann-Hilbert problem;    Factorization theory;    Almost periodic function;   

DOI  :  10.1016/j.jmaa.2015.07.028

来源: Elsevier

【 摘 要 】

We solve a Riemann-Hilbert problem with almost periodic coefficient G, associated to a Toeplitz operator T-G in a class which is closely connected to finite interval convolution equations, based on a generalization of the so-called table method. The explicit determination of solutions to that problem allows one to establish necessary and sufficient conditions for the invertibility of the corresponding Toeplitz operator, and to determine an appropriate factorization of G, providing explicit formulas for the inverse of T-G. Some unexpected properties of the Fourier spectrum of the solutions are revealed which are not apparent through other approaches to the same problem. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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