187 research outputs found
Positive definite collections of disks
Let . M. Putinar
and B. Gustafsson proved recently that the matrix , , is positive definite if disks form a disjoint collection. We
extend this result on symmetric collections of discs with overlapping. More
precisely, we show that in the case when the nodes are situated at the
vertices of a regular -gon inscribed in the unit circle and , the matrix is positive definite if and only if
, where is the smallest zero of the Jacobi
polynomial , .Comment: 24 page
Sharp pointwise gradient estimates for Riesz potentials with a bounded density
We establish sharp inequalities for the Riesz potential and its gradient in
and indicate their usefulness for potential analysis, moment
theory and other applications.Comment: 14 pages, submitted to Analysis and Mathematical Physic
V.M. Miklyukov: from dimension 8 to nonassociative algebras
In this short survey we give a background and explain some recent
developments in algebraic minimal cones and nonassociative algebras. A good
deal of this paper is recollections of my collaboration with my teacher, PhD
supervisor and a colleague, Vladimir Miklyukov on minimal surface theory that
motivated the present research. This paper is dedicated to his memory.Comment: 19 page
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