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μ -Hankel operators on Hilbert spaces

Mirotin Adolf, Kuzmenkova Ekaterina

Opuscula Mathematica

2021

Vol. 41, no. 6

881--898

A class of operators is introduced (μ -Hankel operators, μ 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 |μ| = 1 their description in the Hardy space is given. Integral representations of ^-Hankel operators on the unit disk and on the Semi-Axis are also considered.

Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

Verma Amit K., Gupta Bivek

Opuscula Mathematica

2021

Vol. 41, no. 5

701--723

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.

Operator representations of function algebras and functional calculus

Juratoni A., Suciu N.

Opuscula Mathematica

2011

Vol. 31, no. 2

237-255

This paper deals with some operator representations φ of a weak*-Dirichlet algebra A, which can be extended to the Hardy spaces Hp(m), associated to A and to a representing measure m of A, for 1 ≤ p ≤ ∞. A characterization for the existence of an extension φp of φ to Lp(m) is given in the terms of a semispectral measure Fφ of φ. For the case when the closure in Lp(m) of the kernel in A of m is a simply invariant subspace, it is proved that the map φp/Hp(m) can be reduced to a functional calculus, which is induced by an operator of class Cρ in the Nagy-Foias sense. A description of the Radon-Nikodym derivative of Fφ is obtained, and the log-integrability of this derivative is proved. An application to the scalar case, shows that the homomorphisms of A which are bounded in Lp(m) norm, form the range of an embedding of the open unit disc into a Gleason part of A.