Interpolation and absolutely convergent series in Fréchet spaces. (January 2019)

• Record Type: Journal Article
• Authors: Merzlyakov, S. G.
• Is Part Of: Sbornik. Volume 210:Number 1(2019)
• Page Start: 105
• Page End: 144
• Publication Date: 2019-01
• Subjects: 41A05; 30B50 -- 46A04 -- 46E10; Fréchet space -- absolutely convergent series -- interpolation -- continuous linear functionals -- spaces of holomorphic functions -- series of exponentials; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8902
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: A theorem due to Eidelheit concerning the interpolation problem for a sequence of continuous linear functionals in a Fréchet space is generalized. A solvability criterion for the interpolation problem is obtained in the form of an absolutely convergent series whose elements are in a fixed set. A solution of the system of equations for a sequence of functionals is constructed explicitly in a particular case. These results are then applied to spaces of holomorphic functions. Bibliography: 15 titles.