A class of Hausdorff-Zhu operators

被引：11

作者：

Karapetyants, Alexey ^{[1
,2
]}

Mirotin, Adolf ^{[2
,3
]}

机构：

[1] Southern Fed Univ, Inst Math Mech & Comp Sci, Rostov Na Donu 344090, Russia

[2] Southern Fed Univ, Reg Math Ctr, Rostov Na Donu 344090, Russia

[3] Franc Skorina Gomel State Univ, Dept Math & Programming Technol, Gomel 246019, BELARUS

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 03期

关键词：

Hausdorff operators; Bergman and Hardy spaces; Radial operator; Finite dimensional operator;

D O I：

10.1007/s13324-022-00681-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce and study a special class of Hausdorff operators, we call this class "Hausdorff-Zhu operators", on Banach spaces of analytic functions in the unit disc. Conditions of boundedness, compactness, and nuclearity of these operators are given. A special attention is paid to particular but important cases of analytic symbols and radial symbols. In particular it is shown that Hausdorff-Zhu operators with analytic symbols are at most two-dimensional and their spectra are computed.

引用

页数：19

共 19 条

[1]

Achieser N.I., 1977, Theorie der linearen Operatoren im Hilbert-Raum

[2]

Defant A., 1993, N HOLLAND MATH STUD, V176

[3] ON MULTIPLIERS OF HP SPACES [J].

DUREN, PL .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 22 (01) :24-&

[4]

Duren PL., 1970, THEORY SPACES

[5]

Duren PL, 2004, Mathematical Surveys and Monographs

[6]

Hardy G.H., 1988, POLYA INEQUALITIES, V2nd

[7]

Hedenmalm H., 2000, Theory of Bergman spaces. Graduate Texts in Mathematics, DOI DOI 10.1007/978-1-4612-0497-8

[8]

Heil C, 2011, APPL NUMER HARMON AN, P3, DOI 10.1007/978-0-8176-4687-5_1

[9]

Karapetiants N., 2001, Equations with Involutive Operators, DOI 10.1007/978-1-4612-0183-0

[10]

Karapetyants A., MATH METHOD APPL SCI, V43

← 1 2 →