Weighted 𝜕-Integral Representations of 𝐶𝟏-Functions in 𝐶𝑛

Weighted ๐œ•-Integral Representations of ๐ถ๐Ÿ-Functions in ๐ถ๐‘›

For ๐ถ1-functions ๐‘“, given in the complex space ๐ถ๐‘›, integral representations of the form ๐‘“=๐‘ƒ(๐‘“)โˆ’๐‘‡(๐œ•๐‘“) are obtained. Here, ๐‘ƒ is the orthogonal projector of the space ๐ฟ2{๐ถ๐‘›;๐‘’โˆ’๐œŽ|๐‘ง|๐œŒ|๐‘ง|๐›พ๐‘‘๐‘š(๐‘ง)} onto its subspace of entire functions and the integral operator ๐‘‡ appears by means of explicitly constructed ke...

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Bibliographic Details
Main Author: Arman H. Karapetyan
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2012/265092
Description
Summary:For ๐ถ1-functions ๐‘“, given in the complex space ๐ถ๐‘›, integral representations of the form ๐‘“=๐‘ƒ(๐‘“)โˆ’๐‘‡(๐œ•๐‘“) are obtained. Here, ๐‘ƒ is the orthogonal projector of the space ๐ฟ2{๐ถ๐‘›;๐‘’โˆ’๐œŽ|๐‘ง|๐œŒ|๐‘ง|๐›พ๐‘‘๐‘š(๐‘ง)} onto its subspace of entire functions and the integral operator ๐‘‡ appears by means of explicitly constructed kernel ฮฆ which is investigated in detail.
ISSN:0972-6802
1758-4965

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