On a problem associated with approximation by exponential functions

Abstract

While formalizing a certain problem of numeric signal processing there arises a mathematical problem on approximating a square integrable function defined on some finite interval of the real line by linear combinations of exponential functions. This problem is solved as an optimization problem by means of minimizing the root-mean-square deviation with respect to the coefficients of the linear combination and with respect to the exponents of the exponential functions. In some cases, minimizing with respect to the exponents, a computational singularity occurs due to small denominators. In the present paper this singularity is shown to be removable and a mechanism of its removal is described.