I. Kh. Musin, Z. Yu. Fazullin, R. S. Yulmukhametov, “Convolution equation in space of fast decaying functions on unbounded convex set in <nobr>$\mathbb R^n$</nobr>”, Ufimsk. Mat. Zh., 2025, Volume 17, Issue 4,Pages <nobr>63

Convolution equation in space of fast decaying functions on unbounded convex set in $\mathbb R^n$

I. Kh. Musin^a, Z. Yu. Fazullin^b, R. S. Yulmukhametov^ab

^a Institute of Mathematics, Ufa Federal Research Center, RAS, Chernyshevsky str. 112, 450076, Ufa, Russia
^b Ufa University of Science and Technology, Zaki Validi str. 32, 450077, Ufa, Russia

Abstract: In the work we study the solvability of the convolution equation (in particular, of differential–difference equation) in the Schwartz space on an unbounded convex set in $\mathbb R^n$.

Keywords: schwartz space, fourier — Laplace transform of functionals.

UDC: 517.55

MSC: 46A04

Received: 01.09.2025