ON THE SYMBOL CALCULUS FOR MULTIDIMENSIONAL HAUSDORFF OPERATORS

E. Liflyand, A. Mirotin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The aim of this work is to derive a symbol calculus on L2(Rn) for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorff operator elaborated earlier by the second named author.

Original languageEnglish
Pages (from-to)23-32
Number of pages10
JournalJournal of Mathematical Sciences
Volume280
Issue number1
DOIs
StatePublished - Mar 2024

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Funding

The second author is partially supported by the State Program of Scientific Research of Republic of Belarus, project no. 20211776, and by the Ministry of Education and Science of Russia, agreement no. 075-02-2023-924.

FundersFunder number
State Program of Scientific Research of Republic of Belarus20211776
Ministry of Education and Science of the Russian Federation075-02-2023-924

    Keywords

    • Commutative algebra
    • Commuting family
    • Convolution
    • Fourier transform
    • Fractional power
    • Hausdorff operator
    • Holomorphic function
    • Matrix symbol
    • Positive definiteness
    • Primary 47B38
    • Secondary 42B10
    • Symbol

    Fingerprint

    Dive into the research topics of 'ON THE SYMBOL CALCULUS FOR MULTIDIMENSIONAL HAUSDORFF OPERATORS'. Together they form a unique fingerprint.

    Cite this