q-Titchmarsh-Weyl theory: series expansion
2012 ◽
Vol 205
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pp. 67-118
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AbstractWe establish a q-Titchmarsh-Weyl theory for singular q-Sturm-Liouville problems. We define q-limit-point and q-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jackson q-Bessel functions is given. This example leads to the completeness of a wide class of q-cylindrical functions.
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1980 ◽
Vol 86
(3-4)
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pp. 275-289
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1986 ◽
Vol 103
(3-4)
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pp. 215-228
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1976 ◽
Vol 28
(5)
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pp. 905-914
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2005 ◽
Vol 86
(3)
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pp. 237-248
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1974 ◽
Vol 10
(2)
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pp. 315-316
2000 ◽
Vol 130
(1)
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pp. 25-34
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