arXiv subjects

Vladimir B. Vasilyev

Publications and source records attributed to Vladimir B. Vasilyev.

2 recordsLinked to original sources

arXiv2015

On asymptotical expansions for certain singular integrals: 2-dimensional case

One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these operators. These limit distributions are constructed with a help of the Fourier transform, Dirac mass-function and its derivatives, and well-known distribution related to the Cauchy type integral.

math.AP↗

arXiv2014

Discrete singular integrals in a half-space

We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf Z}^m_{+}$) iff such is its continual analogue. The key point for this consideration takes solvability theory of so-called periodic Riemann boundary problem, which is constructed by authors.

math.AP↗