Annals of Functional Analysis

Interplay of Wiener--Hopf and Hankel operators with almost periodic Fourier symbols on standard and variable exponent Lebesgue spaces

L. P. Castro and A. S. Silva

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Abstract

Wiener--Hopf plus Hankel and Wiener--Hopf minus Hankel operators in both frameworks of standard and variable exponent Lebesgue spaces are considered in this paper. The main aim is to describe certain dependencies between the Fredholm property of some Wiener--Hopf operators acting between variable exponent Lebesgue spaces and the invertibility of Wiener--Hopf plus and minus Hankel operators on all the standard Lebesgue spaces. Different types of Fourier symbols will be used but special focus will be considered on the Wiener subclass of almost periodic matrix functions. In the first part of the paper we will give a survey of investigations on related results. This will be useful at the end of the paper to derive the above mentioned dependencies between the operators under study.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 2 (2015), 49-59.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1418997765

Digital Object Identifier
doi:10.15352/afa/06-2-5

Mathematical Reviews number (MathSciNet)
MR3292514

Zentralblatt MATH identifier
1312.47033

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A20: Dilations, extensions, compressions 42A75: Classical almost periodic functions, mean periodic functions [See also 43A60]

Keywords
Wiener--Hopf operator Hankel operator almost periodic function Fredholm property invertibility

Citation

Castro, L. P.; Silva, A. S. Interplay of Wiener--Hopf and Hankel operators with almost periodic Fourier symbols on standard and variable exponent Lebesgue spaces. Ann. Funct. Anal. 6 (2015), no. 2, 49--59. doi:10.15352/afa/06-2-5. https://projecteuclid.org/euclid.afa/1418997765


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