The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem

2025/08/14 by Micheas, Athanasios Christou
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.10662

Abstract

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases.

Citations

• The Taylor Measure and its Applications
• Classical orthogonal polynomials revisited
• Zeros of Gaussian power series, Hardy spaces and determinantal point processes
• A Bayes-Sard Cubature Method
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• Probabilistic ODE Solvers with Runge-Kutta Means
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