On the theory of class p operators and generalizations

Abstract

Motivated by integral-free representations of solutions of complex second-order partial differential equations L_u = 0 obtained from class P Bergman integral operators, we introduce a new type of infinite series (“P-series”) and show that their theory is an analog of the usual Bergman theory in integral form, of the same generality and in certain applications of greater utility. A basic spinoff of this theory is a novel kind of criterion for L [d] class P

Keywords:

• Second-order complex partial differential equations
• representation of solutions
• class P Bergman operators
• generalization of class P operators
• series solutions
• Bergman differential operators
• approximate solutions

AMS(MOS):

• 35C10
• 35C15
• Herrn Professor Dr. CURT SCHMIEDEN Zum 85. Geburtstag in Dankbarkeit gewidmet

^†Research Supported in part by NSERC under Grant A9097

^†Research Supported in part by NSERC under Grant A9097

Notes

^†Research Supported in part by NSERC under Grant A9097