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On the description of multidimensional normal Hausdorff operators on Lebesgue spaces

  • Adolf R. Mirotin ORCID logo EMAIL logo
Published/Copyright: September 18, 2019

Abstract

Hausdorff operators originated from some classical summation methods. Now this is an active research field. In the present article, a spectral representation for multidimensional normal Hausdorff operator is given. We show that normal Hausdorff operator in L2(n) is unitary equivalent to the operator of multiplication by some matrix-valued function (its matrix symbol) in the space L2(n;2n). Several corollaries that show that properties of a Hausdorff operator are closely related to the properties of its symbol are considered. In particular, the norm and the spectrum of such operators are described in terms of the symbol.

MSC 2010: 47B38; 47B15; 46E30

Communicated by Siegfried Echterhoff


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Received: 2019-04-11
Published Online: 2019-09-18
Published in Print: 2020-01-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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