Abstract:
We consider a generalization of Hausdorff operator and introduce the notion of the symbol of such an operator. Using this notion we describe under some natural conditions the structure and investigate important properties (such as invertibility, spectrum, norm, and compactness) of normal generalized Hausdorff operators on Lebesgue spaces over $\mathbb{R}^n.$ The examples of Cesàro operators are considered.
Keywords:
Hausdorff operator, Cesàro operator, symbol of an operator, normal operator, spectrum, compact operator.
\Bibitem{Mir19}
\by A.~R.~Mirotin
\paper On the stricture of normal Hausdorff operators on Lebesgue spaces
\jour Funktsional. Anal. i Prilozhen.
\yr 2019
\vol 53
\issue 4
\pages 27--37
\mathnet{http://mi.mathnet.ru/faa3645}
\crossref{https://doi.org/10.4213/faa3645}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4043291}
Linking options:
https://www.mathnet.ru/eng/faa3645
https://doi.org/10.4213/faa3645
https://www.mathnet.ru/eng/faa/v53/i4/p27
This publication is cited in the following 2 articles:
Karapetyants A., Liflyand E., “Defining Hausdorff Operators on Euclidean Spaces”, Math. Meth. Appl. Sci., 43:16 (2020), 9487–9498
A. R. Mirotin, “A Hausdorff operator with commuting family of perturbation matrices is a non-Riesz operator”, Russ. J. Math. Phys., 27:4 (2020), 484–490
Citation in format AMSBIB
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