We study heat kernels of locally finite graphs and discrete heat equation morphisms. These are combinatorial analogs to heat equation morphisms in Riemannian geometry (cf. E. Loubeau, [10]), parallel closely the discrete harmonic morphisms due to H. Urakawa, [13], and their properties are related to the initial value problem for the discrete heat equation. In applications we consider Hamming graphs (using the discrete Fourier calculus on Z_2^N), establish a heat kernel comparison theorem, and study the maps of e-nets induced by heat equation morphisms among two complete Riemannian manifolds. KEYWORDS: Combinatorial Laplacian, discrete heat equation, heat equation morphism, Hamming graph, discrete Fourier transform
Discrete Heat Equation Morphisms / Abatangelo, Vito; Dragomir, S.. - In: INTERDISCIPLINARY INFORMATION SCIENCES. - ISSN 1340-9050. - 14:2(2008), pp. 225-244. [10.4036/iis.2008.225]
Discrete Heat Equation Morphisms
ABATANGELO, Vito;
2008-01-01
Abstract
We study heat kernels of locally finite graphs and discrete heat equation morphisms. These are combinatorial analogs to heat equation morphisms in Riemannian geometry (cf. E. Loubeau, [10]), parallel closely the discrete harmonic morphisms due to H. Urakawa, [13], and their properties are related to the initial value problem for the discrete heat equation. In applications we consider Hamming graphs (using the discrete Fourier calculus on Z_2^N), establish a heat kernel comparison theorem, and study the maps of e-nets induced by heat equation morphisms among two complete Riemannian manifolds. KEYWORDS: Combinatorial Laplacian, discrete heat equation, heat equation morphism, Hamming graph, discrete Fourier transformI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
