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On the pointwise convergence of the eigenfunction expansion associated with some iterated boundary value problems

Authors: Jyoti Das and Prabir Kumar Sen Gupta
Journal: Proc. Amer. Math. Soc. 98 (1986), 593-600
MSC: Primary 34B25; Secondary 47E05
MathSciNet review: 861757
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Abstract: Given a boundary value problem consisting of a second-order differential equation and some boundary conditions, one can derive higher-order boundary value problems, called iterated boundary value problems, provided the coefficients in the second-order differential equation are sufficiently smooth. The problem of convergence of the eigenfunction expansions associated with boundary value problems of even order has been the central attraction for mathematicians since the beginning of this century. The idea of this paper is to single out some higher-order boundary value problems, for which the question of convergence of the said expansion is completely answered by the similar problem associated with the second-order boundary value problem responsible for the generation of the iterated boundary value problem.

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Keywords: Bilinear concomitant, boundary condition function, boundary value problem, convergence under Fourier conditions, Hilbert space, Lebesgue square-integrable solution, limit-point case at infinity, limit-$ n$ case at infinity, resolvent operator, simple closed contour
Article copyright: © Copyright 1986 American Mathematical Society

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