André Kowacs | Searcharxiv

arXiv2024

Exponential Taylor Series

This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{λx})$, where $λ\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an infinite series to $C^\infty$ functions, which is shown to recover the original function under suitable conditions on the remainder. These results are also used to calculate some infinite series involving Stirling Numbers, as well as providing a few examples.

math.CA↗

arXiv2024

Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds

We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp Gårding inequality for compact homogeneous vector bundles and compact homogeneous manifolds. The sharp Gårding inequality is the strongest lower bound estimate known to hold for systems on $\mathbb{R}^n$, and the aim of this paper is to extend this property to systems on compact Lie groups and compact homogeneous manifolds. Our results extend previous works by Lax and Nirenberg [Comm. Pure Appl. Math., Vol. 8, 129-209, (1966)], and by Ruzhansky and Turunen [J. Funct. Anal., Vol. 267, 144-172, (2011)]. As an application, we establish existence and uniqueness of solution to a class of systems of initial value problems of pseudo-differential equations on compact Lie groups and compact homogeneous manifolds.

math.AP↗