Functional Analytic Methods for Heat Green Operators

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Focusing on the intersection of heat equations and differential geometry, this monograph employs functional analysis and the Weyl-Hörmander calculus to explore heat Green operators under various boundary conditions. It emphasizes constructive methods in partial differential equations, providing detailed examples and applications related to elliptic and parabolic problems. The text is designed for a wide audience, presenting complex ideas clearly to facilitate understanding of initial boundary value problems and their implications in mathematics and probability.