M H Annaby and Z S Mansour 2005 J. Phys. A: Math. Gen. 38 3775 doi:10.1088/0305-4470/38/17/005
M H Annaby and Z S Mansour
Show affiliationsThis paper is devoted to studying a q-analogue of Sturm–Liouville eigenvalue problems. We formulate a self-adjoint q-difference operator in a Hilbert space. Some of the properties of the eigenvalues and the eigenfunctions are discussed. Green's function is constructed and the problem in question is inverted into a q-type Fredholm integral operator with a symmetric kernel. The set of eigenfunctions is shown to be a complete orthogonal set in the Hilbert space. Examples involving basic trigonometric functions are involved.
34L10 Eigenfunction expansions, completeness of eigenfunctions
39A13 Difference equations, scaling (q-differences) (See also 33Dxx)
Issue 17 (29 April 2005)
Received 24 December 2004, in final form 3 March 2005
Published 13 April 2005
A Corrigendum for this article has been published in 2006 J. Phys. A: Math. Gen. 39 8747
M H Annaby and Z S Mansour 2005 J. Phys. A: Math. Gen. 38 3775
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