On the expansion problem of a function associated with a system of second order differential equations
Abstract
In the present paper we generalize the Parseval theorem and the expansion theorem for a function f(x) = (f1(x), f2(x))T satisfying fT(x)R(x)f(x) ∈ L (-∞, ∞) associated with the above system of second order differential equations under the general boundary conditions, where the elements of R(x) i.e. s(x), t(x) are assumed to be greater than zero for x ∈ (a, b), a, b being finite or infinite.
Copyright © 2013 Debasish Sengupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
D. Sengupta, On the expansion problem of a function associated with a system of second order differential equations, J. Math. Comput. Sci. 3 (2013), 1565–1585.
BibTeX
@article{Sengupta2013,
author = {Sengupta, Debasish},
title = {On the expansion problem of a function associated with a system of second order differential equations},
journal = {J. Math. Comput. Sci.},
volume = {3},
year = {2013},
pages = {1565--1585},
doi = {}
}