Year: 2017
Type: article
Abstract: We consider the Hilbert space 𝐹 2 𝜙 of entire functions of 𝑛 variables constructed by means of a convex function 𝜙 in C 𝑛 depending on the absolute value of the variable and growing at infinity faster than 𝑎|𝑧| for each 𝑎 > 0. We study the problem on describing the dual space in terms of the Laplace transform of the functionals.Under certain conditions for the weight function 𝜙, we obtain the description of the Laplace transform of linear continuous functionals on 𝐹 2 𝜙 .The proof of the main result is based on using new properties of Young-Fenchel transform and one result on the asymptotics of the multi-dimensional Laplace integral established by R.A. Bashmakov, K.
Source: Ufimskii Matematicheskii Zhurnal
Author: Il'dar Khamitovich Musin
Institution: Institute of Mathematics with Computer Center
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2766447243