Separation of variables and alternative representations for non-selfadjoint boundary value problems

Abstract

The technique of separation of variables has not yet been fully exploited. It can be used to obtain solutions of non-selfadjoint problems in partial differential equations by making use of spectral representations associated with non-selfadjoint ordinary differential equations. In addition, it can often be used to obtain alternative representations which arc more rapidly convergent and from which asymptotic expansions of solutions with respect to parameters can be found.

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