2016/12/18 by S. G. Merzlyakov, Merzlyakov, S. G., S. V. Popenov +1
Mathematics · #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1612.05972
openalex publication_date 2016/12/18 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the problem in the case when all infinite portions of interpolation nodes are situated on a finite system of rays. It is also disclosed that the problem is equivalent to particular problems of simple interpolation, as well as of point-wise crude approximation, by sums of the series of exponentials.