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), 593600
MSC:
Primary 34B25; Secondary 47E05
MathSciNet review:
861757
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Abstract: Given a boundary value problem consisting of a secondorder differential equation and some boundary conditions, one can derive higherorder boundary value problems, called iterated boundary value problems, provided the coefficients in the secondorder 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 higherorder boundary value problems, for which the question of convergence of the said expansion is completely answered by the similar problem associated with the secondorder boundary value problem responsible for the generation of the iterated boundary value problem.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198608617571
PII:
S 00029939(1986)08617571
Keywords:
Bilinear concomitant,
boundary condition function,
boundary value problem,
convergence under Fourier conditions,
Hilbert space,
Lebesgue squareintegrable solution,
limitpoint case at infinity,
limit case at infinity,
resolvent operator,
simple closed contour
Article copyright:
© Copyright 1986
American Mathematical Society
