3 papers
math.FA2025
On a unique two-dimensional integral operator homogeneous with respect to all orientation preserving linear transformations
Zhirayr Avetisyan, Alexey Karapetyants, Adolf Mirotin
In this paper, we consider a two-dimensional operator with an antisymmetric integral kernel, recently introduced by Z. Avetisyan and A. Karapetyants in connection to the study of g…
math.FA2024
Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators
Zhirayr Avetisyan, Alexey Karapetyants, Irina Smirnova
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions…
math.FA2024
Mixed-Fourier-norm spaces and holomorphic functions
Zhirayr Avetisyan, Alexey Karapetyants
We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group . Namely, on a domain of the form we introdu…