A. Katsevich

activity

20162021

collaborators

Showing math.FAShow all

2 papers · 1 filter

math.FA2020

On the spectral properties of the Hilbert transform operator on multi-intervals

Marco Bertola, Alexander Katsevich, Alexander Tovbis

Let $J, E \subset R$ be two multi-intervals with non-intersecting interiors. Consider the following operator $$A:\, L^2( J )\to L^2(E),\ (Af)(x) = \frac 1π\int_{ J } \frac {f(…

math.FA2018

Inversion formula and range conditions for a vector multi-interval finite Hilbert transform in $L^{2}$

Alexander Katsevich, Marco Bertola, Alexander Tovbis

Given $n$ disjoint intervals $I_{j}$ , on $R$ together with $n$ functions $ψ_{j} \in L^{2} (I_{j})$ , $j = 1, \dots n$ , and an $n \times n$ matrix $Θ$ , the problem is to find an $L^{2}$ solu…

On the spectral properties of the Hilbert transform operator on multi-intervals

Inversion formula and range conditions for a vector multi-interval finite Hilbert transform in L2

Inversion formula and range conditions for a vector multi-interval finite Hilbert transform in $L^{2}$