Ryuichi Ishimura: Existence and prolongation of analytic solutions of non-local differential equations, p.179-197

Abstract:

In this paper, we prove the general invertibility theorem for non-local pseudo-differential operators and using this, we establish the theorems of analytic continuation and of existence of holomorphic solutions to non-local differential equations. We also obtain a concrete method to construct a holomorphic solutions to constant coefficient equations.

Key Words: Pseudo-differential operators, partial differential equations of infinite ordre, non-local equations, differential-difference equations.

2000 Mathematics Subject Classification: Primary: 35S99;
Secondary: 35R50, 35A27.

Download the paper in pdf format here.