Convolution of vector-valued distributions: A survey and comparison
Volume 495 / 2013
Dissertationes Mathematicae 495 (2013), 1-51
MSC: 46F05, 46F10, 46A32, 46E10.
DOI: 10.4064/dm495-0-1
Abstract
We overview the literature concerning bilinear operations on vector-valued distributions in general, and more specifically the convolution of vector-valued functions or distributions. We compare and evaluate the different approaches to this problem of L. Schwartz on the one hand and of Y. Hirata and R. Shirarishi on the other. Moreover we discuss applications of the general existence and uniqueness results to different branches of mathematical analysis like partial differential equations or harmonic analysis.
