2 citations · 4 across the 5 of their papers we have counts for
5 papers
At Most Two Radii Theorem For A Real Eigenvalue Of The Hyperbolic Laplacian
Sergei Artamoshin
We study a -dimensional hyperbolic space of a negative constant sectional curvature . Let be a real eigenvalue and be an eigenfunction of the hyperbo…
One Radius Theorem For A Radial Eigenfunction Of A Hyperbolic Laplacian
Sergei Artamoshin
Let us fix two different radial eigenfunctions of a hyperbolic Laplacian and assume that both of them have the same value at the origin. Both eigenvalues can be complex numbers. Th…
The Spherical Ratio of Two Points and its Integral Properties
Sergei Artamoshin
At the end of 19-th century, 1874, Hermann Schwartz found that for every point inside a planar disk, a two-dimensional Poisson Kernel can be written as a ratio of two segments, whi…
Lower Bounds For The First Eigenvalue Of The Laplacian With Dirichlet Boundary Conditions In A Hyperbolic Space Of A Negative Constant Curvature
Sergei Artamoshin
In this paper we consider a domain in a space of negative constant sectional curvature. Such assumption about the sectional curvature let us develop a new technique and improve exi…
Geometric Interpretation of the two dimensional Poisson Kernel and its applications
Sergei Artamoshin
Hermann Schwarz, while studying complex analysis, introduced the geometric interpretation for the Poisson kernel in 1890. We shall see here that the geometric interpretation can be…