The Taylor Integral and a Generalization of the Discrete Fourier Transform

Abstract

We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the discrete Fourier transform, and we identify general conditions for it to be invertible when applied to any real or complex sequence. Applications to the mathematical sciences are also presented.

44 pages, 3 figures, 3 tables. Keywords: Computer Graphics; Cryptography; Difference Equations; Discrete Fourier Transform; Discrete Taylor Transformation; Taylor Measure; Taylor Integral; Vandermonde matrix inversion