Multiband sampling theorems for Mittag-Leffler transforms bandlimited on rays

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.

KEYWORDS:

• Riemann–Liouville fractional calculus
• fractional integro-differential equations
• analytic Kramer sampling theorem

AMS SUBJECT CLASSIFICATION:

• 26A33
• 33E20
• 42A38
• 44A05
• 94A12

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by Alexander von Humboldt-Stiftung Foundation under the grants 3.4-JEM/1142916 and 3.4-EGY/1039259.