The heat kernel on a finite graph in different Time-scales

Authors

YANG CHENFollow
JAY JORGENSONFollow
LUIS LOPEZFollow
LEJLA SMAJLOVICFollow

Author ORCID Identifier

YANG CHEN: 0009-0002-7364-5777

JAY JORGENSON: 0000-0002-9765-0944

LUIS LOPEZ: 0009-0007-5192-7163

LEJLA SMAJLOVIC: 0000-0002-2709-5535

DOI

10.55730/1300-0098.3544

Abstract

Let G be a finite, weighted graph, and let [[EQUATION]] be a Time-scale with a fixed point [[EQUATION]] such that sup[[EQUATION]]. In this paper we construct the heat kernel on G in Time-scale [[EQUATION]] in terms of a certain convolution series involving he heat operator acting on a parametrix, which is a fairly general function depending on the vertex set of G and the time variable [[EQUATION]]. We develop some applications by choosing different parametrices and various Time-scales. The results we obtain here do extend, in part, aspects of the recent articles in that the Time-scale considered in this paper is arbitrary.

Keywords

Heat kernel, finite graph, time-scales

First Page

840

Last Page

860

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

CHEN, YANG; JORGENSON, JAY; LOPEZ, LUIS; and SMAJLOVIC, LEJLA (2024) "The heat kernel on a finite graph in different Time-scales," Turkish Journal of Mathematics: Vol. 48: No. 5, Article 3. https://doi.org/10.55730/1300-0098.3544
Available at: https://journals.tubitak.gov.tr/math/vol48/iss5/3