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Bibliographic Details
Main Authors: Fjordholm, Ulrik S., Karlsen, Kenneth H., Pang, Peter H. C.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.18649
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Table of Contents:
  • We develop a parametrix approach for constructing solutions and establishing grid-size independent estimates for semi-discrete heat equations with variable coefficients. While the classical continuous setting benefits from Gaussian estimates of the constant coefficient heat kernel, such estimates are not available in the semi-discrete context. To address this complication, we derive estimates involving products of heavy-tailed Lorentz (also known as Cauchy) probability densities. These Lorentzian estimates provide a sufficient handle on certain iterated convolutions involving Bessel functions, enabling us to achieve convergence of the parametrix approach.