Adolf Mirotin
Dr.
Department of Mathematics and Programming Technologies, Francisk Skorina Gomel State University, Gomel, Belarus and
Regional Mathematical Center of Southern
Federal University, Rostov-on-Don, Russia
1
Research interests
Operator theory
- semigroups of operators,
- functional (operator) calculi,
- Hankel and Toeplitz operators,
- Hausdorff operators.
- Harmonic analysis on topological groups,
- Harmonic analysis on topological semigroups,
2
Projects supported by the Regional Mathematical Center
µ-Hankel operators on Hilbert spaces.
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 µ-Hankel operators on the unit disc and on the Semi-Axis are also considered.
Boundedness of Hausdorff operators on hardy spaces over homogeneous spaces of Lie groups.
The aim of this note is to give boundedness conditions for Hausdorff operators on Hardy spaces H1 with the norm defined via (1, q) atoms over homogeneous spaces of Lie groups with doubling property and to apply the obtained results to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres.
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 µ-Hankel operators on the unit disc and on the Semi-Axis are also considered.
Boundedness of Hausdorff operators on hardy spaces over homogeneous spaces of Lie groups.
The aim of this note is to give boundedness conditions for Hausdorff operators on Hardy spaces H1 with the norm defined via (1, q) atoms over homogeneous spaces of Lie groups with doubling property and to apply the obtained results to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres.
The international scientific conference “Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis - 2022 (OTHA 2022)” was held on 21 - 26 August 2022 in Southern Federal University, Russia. The conference is an official satellite conference to the International Congress of Mathematicians 2022. Adolf - On M-Hankel Operators.
OTHA-2021
Mirotin Adolf
The conference “Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis-X (OTHA 2021)”.
Mirotin Adolf - Hausdorff operators over homogeneous spaces.
Mirotin Adolf - Hausdorff operators over homogeneous spaces.
OTHA-2021
Mirotin Adolf
The international scientific offline workshop OTHA Fall 2021 on
operator theory and harmonic analysis and their applications (14-16 December 2021, Southern Federal University, Rostov-on-Don, Russia)
Mirotin Adolf - Hausdorff operators over compact Abelian groups.
operator theory and harmonic analysis and their applications (14-16 December 2021, Southern Federal University, Rostov-on-Don, Russia)
Mirotin Adolf - Hausdorff operators over compact Abelian groups.
OTHA Fall 2021
Mirotin Adolf
In Focus
