On Some Weighted Hardy Type Classes of One-Parametric Holomorphic Functions. II. Partial Volterra Operators in Parameter

Some classes of partial Volterra operators acting (with respect to a real variable) on a function of one complex and one real variable are explored. The case when the operator kernels depend additionally on a complex parameter is also considered. It is proved that Volterra operators from these class...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 222; no. 2; pp. 374 - 396
Main Author Mikhailov, S.E
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.06.1998
Elsevier
Subjects
Exact sciences and technology
Integral equations
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Several complex variables and analytic spaces
Holomorphic function
Convolution
Resolvent
Volterra integral equations
Complex variable function
Mellin transformation
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Summary:Some classes of partial Volterra operators acting (with respect to a real variable) on a function of one complex and one real variable are explored. The case when the operator kernels depend additionally on a complex parameter is also considered. It is proved that Volterra operators from these classes and the resolvent operators act in weighted Hardy type classes of one parametric holomorphic functions defined on a wedge or on a strip of the complex plane. Moreover, the Volterra operators commutate with the Mellin operators in these classes. The half line Paley–Wiener theorem for the resolvent of the Volterra operator is extended to operators with parameter. Volterra operators tending to operators of the convolution type as well as Volterra operators with fading memory are studied too.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1997.5846