μ-Hankel operators on Hilbert spaces

Abstract

A class of operators is introduced (\(\mu\)-Hankel operators, \(\mu\) is a complex parameter), which generalizes the class of Hankel operators. Criteria for boundedness, compactness, nuclearity, and finite dimensionality are obtained for operators of this class, and for the case \(|\mu| = 1\) their description in the Hardy space is given. Integral representations of \(\mu\)-Hankel operators on the unit disk and on the Semi-Axis are also considered.

Keywords

• hankel operator
• \(\mu\)-hankel operator
• hardy space
• integral representation
• nuclear operator
• integral operator