Synthesis of complete orthonormal fractional bases

Abstract

In this paper, fractional orthonormal basis functions which generalize the well-known fixed pole rational basis functions are synthesized. For a range of non-integer differentiation orders and under mild restrictions on the choice of the basis poles, the synthesized basis functions are complete in the space of functions which are analytic on the open right-half plane and square-integrable on the imaginary axis. This presents an extension of the completeness results for the fractional Laguerre and Kautz bases to fractional orthonormal bases with prescribed pole locations.