The Heat Kernel on Hyperbolic Space

The heat kernel on R

Dirichlet-neumann Kernel for Hyperbolic-dissipative System in Half-space

The purpose of the present paper is to initiate a systematic study of the relation of the boundary values for hyperbolic-dissipative systems of partial differential equations. We introduce a general framework for explicitly deriving the boundary kernel for the Dirichlet-Neumann map. We first use the Laplace and Fourier transforms, and the stability consideration to derive the Master Relationshi...

Universal Approximator Property of the Space of Hyperbolic Tangent Functions

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.

Spectral Approximation of the Free-Space Heat Kernel

Many problems in applied mathematics, physics, and engineering require the solution of the heat equation in unbounded domains. Integral equation methods are particularly appropriate in this setting for several reasons: they are unconditionally stable, they are insensitive to the complexity of the geometry, and they do not require the artificial truncation of the computational domain as do finit...

The heat kernel on the torus