Abstract
New convolutions weighted by Hermite functions and their applications
Highlights
We introduce eight new convolutions weighted by multi-dimensional Hermite functions, prove two Young-type inequalities, and exhibit their applications in different subjects
One application consists in the study of the solvability of a very general class of integral equations whose kernel depends on four different functions
Keywords and phrases: Convolution, Young’s inequality, integral equation, Hermite function, normed ring, Wiener’s algebra
Summary
We introduce eight new convolutions weighted by multi-dimensional Hermite functions, prove two Young-type inequalities, and exhibit their applications in different subjects.
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