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

✍ Scribed by S.E Mikhailov

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 286 KB
• Volume: 222
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5846

✦ Synopsis

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.