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# Form Domains and Eigenfunction Expansions for Differential Equations with Eigenparameter Dependent Boundary Conditions

Published:2002-12-01
Printed: Dec 2002
• Paul Binding
• Branko Ćurgus
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## Abstract

Form domains are characterized for regular $2n$-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first $n-1$ derivatives.
 MSC Classifications: 47E05 - Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47) 34B09 - Boundary eigenvalue problems 47B50 - Operators on spaces with an indefinite metric [See also 46C50] 47B25 - Symmetric and selfadjoint operators (unbounded) 34L10 - Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions