Operators of Almost Hadamard Type and Hardy–Littlewood Operator in the Space of Entire Functions of Several Complex Variables

We introduce the class of operators of almost Hadamard type, that is, linear continuous operators that act on a locally convex space containing all polynomials and have the property that the homogeneous polynomials of any given degree form an invariant subspace. The Hadamard-type (diagonal) operator...

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Bibliographic Details
Published inMathematical Notes Vol. 110; no. 1-2; pp. 61 - 71
Main Authors Ivanova, O. A., Melikhov, S. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2021
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Complex variables
Eigenvectors
Entire functions
Linear operators
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Polynomials
Hardy–Littlewood operator
operator of Hadamard type
space of entire functions
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Summary:We introduce the class of operators of almost Hadamard type, that is, linear continuous operators that act on a locally convex space containing all polynomials and have the property that the homogeneous polynomials of any given degree form an invariant subspace. The Hadamard-type (diagonal) operators, for which each monomial is an eigenvector, are a special case of operators of almost Hadamard type. The operators of almost Hadamard type are studied in the space of all entire functions of several complex variables. The results are used to describe all linear operators continuous in this space and commuting in it with the multidimensional analog of the Hardy–Littlewood operator.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434621070063