On the Uniqueness of Solutions of Duhamel Equations

Tapdigoglu R.

FILOMAT, vol.36, no.11, pp.3891-3898, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 11
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2211891t
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.3891-3898
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

We consider the Duhamel equation phi circle star f = g in the subspace C-xy(infinity) = {f is an element of C-infinity ([0, 1] x [0, 1]) : f (x, y) = F(xy) for some F is an element of C-infinity [0,1]} of the space C-infinity ([0,1] x [0,1]) and prove that if phi l(xy=0) not equal 0, then this equation is uniquely solvable in C-xy(infinity). The commutant of the restricted double integration operator W(xy)f (xy) := integral(x)(0) integral(y)(0) f (t tau)d tau dt on C-xy(infinity). is also described. Some other related questions are also discussed.