Tensor products for Gelfand–Shilov and Pilipović distribution spaces

Abstract

We show basic properties on tensor products for Gelfand-Shilov distributions and Pilipović distributions. This also includes the Fubbini's property of such tensor products. We also apply the Fubbini property to deduce some properties for short-time Fourier transforms of Gelfand-Shilov and Pilipović distributions.2010 Mathematics Subject Classification. 46A32, 46Fxx, 46M05.

The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory

“…We notice that the uniqueness assertions in Lemma 2.7 is an immediate consequence of [38,Lemma 2.3] which asserts that if f ∈…”

Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type

“…, and similarly when each S s are replaced by Σ s , S ′ s or by Σ ′ s . (See also [38].) We let F be the Fourier transform which takes the form…”

Kernel theorems for Beurling-Björck type spaces

“…Establishing kernel theorems or the related property of nuclearity for a given class of locally convex spaces are therefore questions of great relevance for the analysis of continuous linear mappings on such spaces. The study of these questions for locally convex spaces of functions defined through high time-frequency localization conditions has attracted much attention in recent times [6,7,9,12,13,22,23,25], particularly due to potential applications in the microlocal analysis of pseudodifferential and localization operators.…”