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math.FA2025
On Toeplitz operators on compact Abelian groups and discrete Wiener--Hopf operators
Adolf Mirotin
This paper introduces the concept of a rotation number for a continuous, non-degenerate two-dimensional vector field (a zero-free complex-valued function) on a compact connected Ab…
math.FA2025
Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces
A. R. Mirotin
For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consider…
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…