Preprint
An explicit construction of heat kernels and Green's functions in measure spaces
ArXiv.org
Cornell University
12/30/2025
DOI: 10.48550/arxiv.2512.24348
Abstract
We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as$L^{1}$ ,$L^{2}$ , and Hilbert spaces, associated to a locally compact Hausdorff space$\mathfrak{X}$with Borel$σ$ -algebra$\mathcal{B}$ , and endowed with additional measure-theoretic data. Our approach is an adaptation of classical work due to Minakshishundaram and Pleijel, and it requires as input a parametrix or small time approximation to the heat kernel. The methodology developed in this article applies to yield new instances of heat kernel constructions, including normalized Laplacians on finite and infinite graphs as well as Hilbert spaces with reproducing kernels.
Details
- Title: Subtitle
- An explicit construction of heat kernels and Green's functions in measure spaces
- Creators
- Palle Jorgensen - University of IowaJay Jorgenson - City College of New YorkLejla Smajlovic - University of Sarajevo
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2512.24348
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Number of pages
- 37 pages
- Language
- English
- Date posted
- 12/30/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9985112982002771
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