On Completeness and Minimality of Random Exponential System in a Weighted Banach Space of Functions Continuous on the Real Line*

Abstract

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.

Random inverse spectral problems and closed random exponential systems

“…We will use the same method applied to random shifts of holomorphic functions from [6,7] and [11]. By this approach, we will show that for a function in the H p space (see [3]) which consists of holomorphic functions in the upper half-plane  + , random shifts of its zeros generate another analytic function in the upper half-plane whose growth and zeros are very similar to the original one.…”

Minimality and Closeure of Random Exponential Systems

“…The probabilistic approach to classical question on exponential systems gives a new insight. Combining the methods of probability theory and function theory, a few facts are known in the case of random exponents(see [1][2][3][4][5]). Motivated by their works, we study the minimality properties and the closure of the random exponential systems in the space.…”