arXiv subjects

Sergey Sadov

Publications and source records attributed to Sergey Sadov.

22 records · Page 2Linked to original sources

arXiv2011

Hausdorff-Young type theorems for the Laplace transform restricted to a ray or to a curve in the complex plane

Let p and q be conjugate exponents, with p in [1,2]. It is shown that the Laplace transform acts boundedly between the Lp space with unit weight on the positive real semiaxis and the Lq space weighted by a well-projected measure (a term defined in the paper) in the right complex half-plane. The operator norm is uniformly bounded over classes of measures with the same "projection constants". Particular cases are arclength measures on some classes of rectifiable curves. In addition, an analog of the Hausdorff-Young inequality in Lorentz spaces is obtained in the case of "wrong" exponents p>2.

math.CA↗

arXiv2005

Numerical study of high frequency asymptotics of the symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems

A high-frequency asymptotics of the symbol of the Dirichlet-to-Neumann map, treated as a periodic pseudodifferential operator, in 2D diffraction problems is discussed. Numerical results support a conjecture on a universal limit shape of the symbol.

physics.comp-ph↗

arXiv2004

On a necessary and sufficient cyclicity condition for a quadrilateral

A convex quadrilateral with sides a,b,c,d, and diagonals p,q is cyclic iff abp-bcq+cdp-daq=0. This condition, in spite of its simplicity, appears to be unnoted and unexpectedly proof-resilient. We employ advanced methods of computer algebra and nonlinear analysis.

math.GM↗

arXiv2004

Markov's Transformation of Series and the WZ Method

In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the Wilf-Zeilberger (WZ) method. We review Markov's work, put it in the context of modern computer-aided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.

math.CA↗