q -Fractional Calculus and Equations pp 73-105 | Cite as
q-Sturm–Liouville Problems
Chapter
First Online:
Abstract
In this chapter we introduce the study held by Annaby and Mansour in (J. Phys. A Math. Gen. 38(17), 3775–3797, 2005) of a self adjoint basic Sturm–Liouville eigenvalue problem in a Hilbert space. The last two sections of this chapter are about the q 2-Fourier transform introduced by Rubin in (J. Math. Anal. Appl. 212(2), 571–582, 1997; Proc. Am. Math. Soc. 135(3), 777–785, 2007), when q lies in a proper subset of (0, 1) and the generalization of Rubin’s q 2-Fourier transform, introduced in (Mansour, Generalizations of Rubin’s q 2-fourier transform and q-difference operator, submitted, 2012) for any q ∈ (0, 1).
Keywords
Orthogonality Relation Liouville Problem Algebraic Simplicity Unique Limit Point Forward Difference Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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