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      Mellin convolution operators in Bessel potential spaces with admissible meromorphic kernels

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          Abstract

          The paper is devoted to Mellin convolution operators with meromorphic kernels in Bessel potential spaces. We encounter such operators while investigating boundary value problems for elliptic equations in planar 2D domains with angular points on the boundary. Our study is based upon two results. The first concerns commutants of Mellin convolution and Bessel potential operators: Bessel potentials alter essentially after commutation with Mellin convolutions depending on the poles of the kernel (in contrast to commutants with Fourier convolution operatiors.) The second basic ingredient is the results on the Banach algebra \(\mathfrak{A}_p\) generated by Mellin convolution and Fourier convolution operators in weighted \(\mathbb{L}_p\)-spaces obtained by the author in 1970's and 1980's. These results are modified by adding Hankel operators. Examples of Mellin convolution operators are considered. The first version of the paper was published in {\em Memoirs on Differential Equations and Mathematical Physics} {\bf 60}, 135-177, 2013. The formulations and proofs there contain fatal errors, which are improved in the present preprint. Part of the results, obtained with V. Didenko, are published in the preprint

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          Author and article information

          Journal
          2015-02-22
          2016-03-27
          Article
          1502.06248
          8025c687-3000-44a0-9f4c-ecd789ba7d91

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          47G30, 45B35, 45E10
          52 pages, 2 figures, Original investigation. arXiv admin note: text overlap with arXiv:1502.02756
          math.AP math.FA math.OA

          Analysis,Functional analysis,Algebra
          Analysis, Functional analysis, Algebra

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