Lebesgue Spaces and Operators with Complex Gaussian Kernels

Abstract

This paper examines the boundedness properties and Parseval-type relations for operators with complex Gaussian kernels over Lebesgue spaces. Furthermore, this study includes an exploration of the Gauss–Weierstrass semigroup, serving as a particular example within the framework of our analysis.

Keywords

• complex Gaussian kernels
• bounded operator
• Parseval-type relations
• Gauss–Weierstrass semigroup