On continuation via polynomials

Abstract

Polynomial expansions of analytic solutions of linear partial differential equations can be the base for results on the continuation of analytic solutions. An example is the one-dimensional heat equation for which this 'continuation via polynomials' was discovered by Widder [8], In the present paper a Banach scales method is used for the discussion of polynomial expansions in a general framework. For two classes of linear partial differential equations it is shown that 'the general expansion results yield results on the continuation of analytic solutions.

Keywords:

• Analytic differential equations
• Banach scales
• polynomial expansions

AMS:

• 35B60
• 35C10

Additional information

Notes on contributors

Wolfgang Watzlawek