On a Hilbert space of entire functions

2017/10/17 by Musin, I. Kh. · 3 citations
#32A15 #32A36 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.06143

Abstract

A weighted Hilbert space F²_φ of entire functions of n variables is considered in the paper. The weight function φ is a convex function on \mathbb Cⁿ depending on modules of variables and growing at infinity faster than a \Vert z \Vert for each a > 0. The problem of description of the strong dual of this space in terms of the Laplace transformation of functionals is studied in the article. Under some additional conditions on φ the space of the Laplace transforms of linear continuous functionals on F²_φ is described. The proof of the main result is based on new properties of the Young-Fenchel transformation and a result of R.A. Bashmakov, K.P. Isaev and R.S. Yulmukhametov on asymptotics of multidimensional Laplace transform.

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• Inverse dynamic problems for canonical systems and de Branges spaces
• On the construction of de Branges spaces for dynamical systems associated with finite Jacobi matrices
• Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions

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