11 citations · 54 across the 23 of their papers we have counts for
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Reproducing Kernel Hilbert Spaces and entropy Kolmogorov numbers on compact Lie Groups
Zhirayr Avetisyan, Michael Ruzhansky, Karina Gonzalez
On a compact Lie group , we consider the reproducing kernel Hilbert space associated with the integral kernel of a left-invariant, positive, symmetric, trace…
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…
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…
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…
A note on the polar decomposition in metric spaces
Zhirayr Avetisyan, Michael Ruzhansky
The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a s…
Elements (functions) that are universal with respect to a minimal system
Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky
We call an element conditionally universal for a sequential convergence space with respect to a minimal system in a continuously and densely e…
Homogeneous operators and homogeneous integral operators
Zhirayr Avetisyan, Alexey Karapetyants
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, hom…
Approximations in with convergent Fourier series
Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky
For a separable finite diffuse measure space and an orthonormal basis of consisting of bounded functions ,…