We prove existence of weak solutions to an eigenvalue Steklov problem defined in a bounded domain with a Lipschitz continuous boundary.

This paper studies a family of Hilbert spaces of real harmonic functions on bounded regions in Rn and will show that, for a range of values of s, they are reproducing kernel Hilbert spaces. The spaces are characterized by their boundary traces and the inner products are defined via their expansions in the harmonic Steklov eigenfunctions of the region. The reproducing kernels will then be descri...

The master field for a subclass of planar diagrams, so called rainbow diagrams, for higher dimensional large N theories is considered. An explicit representation for the master field in terms of noncommutative random variables in the modified interaction representation in the Boltzmannian Fock space is given. A natural interaction in the Boltzmannian Fock space is formulated by means of a ratio...

The Steklov averages (Steklov or integral means) are used in approximation theory of functions different aspects. This article concerns the by using operator cosine function framework. offers a counterpart translation operator, which forms basic concept for modulus continuity and some processes as well. We will show that allows to define very general an abstract Banach space. properties these g...

We construct periodic families of Poincaré spaces. This gives a partial solution to a question posed by Hodgson in the proceedings of the 1982 Northwestern homotopy theory conference. In producing these families, we formulate a recognition principle for Poincaré duality in the case of finite complexes having one top cell that splits of after a single suspension. We also explain how a Z-equivari...

the paper concerns the relations between the relative Manin-Mumford conjecture and Pink’s conjecture on unlikely intersections in mixed Shimura varieties. The variety under study is the 4-dimensional Poincaré biextension attached to a universal elliptic curve. A detailed list of its special subvarieties is drawn up, providing partial verifications of Pink’s conjecture in this case, and two open...

In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is two-dimensional sloshing problem, which a mixed Steklov—Neumann boundary value problem describing small vertical oscillations of ideal fluid in container or canal uniform cross-section. We prove two-term asymptotic formula eigenvalues. part...