Multiband sampling theorems for Mittag-Leffler transforms bandlimited on rays |
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| Authors: | M. H. Annaby R. M. Asharabi |
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| Affiliation: | 1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egyptmhannaby@sci.cu.edu.eg;3. Department of Mathematics, College of Arts and Sciences, Najran University, Saudi Arabia |
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| Abstract: | We derive a biorthogonal Kramer analytic theorem, for integral transforms whose kernels generate biorthogonal bases in Hilbert spaces. The theorem is applied to various integral transforms associated with classes of fractional integro-differential eigenvalue problems, leading to Lagrange-type interpolation sampling theorems, derived by Djrabshian [Harmonic analysis and boundary value problems in the complex domain. Basel: Birkhäuser; 1993]. We work out some concrete examples, illustrating these sampling expansions. |
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| Keywords: | Riemann–Liouville fractional calculus fractional integro-differential equations analytic Kramer sampling theorem |
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