The Foundamental Solution of Weighted Cauchy Problem for One-ordered Fuchsian Type Pseudodifferential Operator

Abstract

In this paper, we begin with introducing two classes of generalized pseudo-homogeneous functions θ^m and T^m studying their basic properties. Then, under the most general hypothesis, we get the global foundamental solution of weighted Cauchy problem for one-order Fuchsian-typc pseudodifferential operator in the frame PsDO whose symbol belongs to C (D, S^m_{1,0}).