on some applications of a special integrodifferential operators

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2012
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Abstract
Let ๐ถ(๐‘›)(๐”ปร—๐”ป) be a Banach space of complex-valued functions ๐‘“(๐‘ฅ,๐‘ฆ) that are continuous on ๐”ปร—๐”ป, where ๐”ป={๐‘งโˆˆโ„‚โˆถ|๐‘ง|<1} is the unit disc in the complex plane โ„‚, and have ๐‘›th partial derivatives in ๐”ปร—๐”ป which can be extended to functions continuous on ๐”ปร—๐”ป, and let ๐ถ๐ด(๐‘›)=๐ถ๐ด(๐‘›)(๐”ปร—๐”ป) denote the subspace of functions in ๐ถ(๐‘›)(๐”ปร—๐”ป) which are analytic in ๐”ปร—๐”ป (i.e., ๐ถ๐ด(๐‘›)=๐ถ(๐‘›)(๐”ปร—๐”ป)โˆฉโ„‹๐‘œ๐‘™(๐”ปร—๐”ป)). The double integration operator is defined in ๐ถ๐ด(๐‘›) by the formula โˆซ๐‘Š๐‘“(๐‘ง,๐‘ค)=๐‘ง0โˆซ๐‘ค0๐‘“(๐‘ข,๐‘ฃ)๐‘‘๐‘ฃ๐‘‘๐‘ข. By using the method of Duhamel product for the functions in two variables, we describe the commutant of the restricted operator ๐‘Šโˆฃ๐ธ๐‘ง๐‘ค, where ๐ธ๐‘ง๐‘ค={๐‘“โˆˆ๐ถ๐ด(๐‘›)โˆถ๐‘“(๐‘ง,๐‘ค)=๐‘“(๐‘ง๐‘ค)} is an invariant subspace of ๐‘Š, and study its properties. We also study invertibility of the elements in ๐ถ๐ด(๐‘›) with respect to the Duhamel product.
Reference Key
saltan2012journalon Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Suna Saltan, Yasemin ร–zel
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Journal Journal of sex research
Year 2012
DOI
10.1155/2012/894527
URL
http://dx.doi.org/10.1155/2012/894527
Keywords
mathematics

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