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q-Sturm–Liouville Problems

  • Mahmoud H. Annaby
  • Zeinab S. Mansour
Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 2056)

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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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mahmoud H. Annaby
    • 1
  • Zeinab S. Mansour
    • 2
  1. 1.Faculty of Science Department of MathematicsCairo UniversityGizaEgypt
  2. 2.Faculty of Science Department of MathematicsKing Saud UniversityRiyadhKingdom of Saudi Arabia

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