Analyticity of the Schrödinger propagator for the affine Laplacian and its applications to sampling and interpolating sequences

期刊论文
出版模式：

开放获取
发表日期：

2025年7月14日

查看全文

Shubham R. Bais

摘要

In this article, we consider the Schrödinger semigroup for the affine Laplacian. We discuss the analytic continuation of this semigroup, and characterize the image of a subspace of $L^2(\mathbb {R})$ $L^{2} (R)$ under this semigroup as a weighted Bergman space. As an application, we characterize the sampling and the interpolating sequences in the newly obtained Bergman space. Consequently, we construct a new example of a frame in a subspace of $L^2(\mathbb {R})$ $L^{2} (R)$ .