The Heat Equation On The Finite Poincare Upper Half-Plane

DeDeo M. R., Velasquez Elinor

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（2021）

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摘要

A differential-difference operator is used to model the heat equation on a finite graph analogue of Poincare's upper half-plane. Finite analogues of the classical theta functions are shown to be solutions to the heat equation in this setting.

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关键词

Finite upper half-plane, combinatorial Laplacian, zonal spherical function, theta function, heat equation, Cayley graph

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