@article {IOPORT.05492140,
    author       = {Abatangelo, Vito and Dragomir, Sorin},
    title        = {Discrete heat equation morphism.},
    year         = {2008},
    journal      = {Interdisciplinary Information Sciences (IIS)},
    volume       = {14},
    number       = {2},
    issn         = {1340-9050},
    pages        = {225-244},
    publisher    = {Tohoku University, Graduate School of Information Sciences, Sendai},
    doi          = {10.4036/iis.2008.225},
    abstract     = {Summary: 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. {\it E. Loubeau}, Ann. Global Anal. Geom. 15, No.~6, 487--496 (1997; Zbl 0910.58009)], parallel closely the discrete harmonic morphisms due to {\it H. Urakawa} [Glasg. Math. J. 42, No.~3, 319--334 (2000; Zbl 1002.05049)], 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 $\Bbb Z_2^N$), establish a heat kernel comparison theorem, and study the maps of $\varepsilon$-nets induced by heat equation morphisms among two complete Riemannian manifolds.},
    identifier   = {05492140},
}