Factorization of Conservative Integral Convolution Type Operators with Slowly Decaying Kernels

Abstract

Factorization of Conservative Integral Convolution Type Operators with Slowly Decaying Kernels L. G. Arabadzhyan Armenian State Pedagogical University, Erevan, Armenia Received September 23, 1999 1◦. A method for solving convolution type equations (in particular, Wiener–Hopf equations) on the basis of the Volterra factorization of integral operators and the analysis of the nonlinear functional factorization equations was suggested in [1–5]. Let R ≡ [0,+∞), and let E (R) be one of the spaces Lp (R), p ≥ 1, and M (R). By J we denote the identity operator in E (R), and by K we denote the Wiener–Hopf integral operator (K f)(x) = ∞ ∫