Iterates of operators and Gelfand-Shilov classes

作者：Calvo Daniela; Rodino Luigi^*

来源：Integral Transforms and Special Functions, 2011, 22(4-5): 269-276.

DOI：10.1080/10652469.2010.541037

• Gelfand-Shilov spaces
• iterates of operators
• partial differential operators with polynomial coefficients
• generalized hypergeometric functions
• G-functions

The aim of this paper is to characterize Gelfand-Shilov classes S(mu)(mu), for mu >= 1/2, in terms of the iterates of a globally elliptic operator P with polynomial coefficients. Namely, we consider operators of Shubin type globally defined in R(n), for which L(2)-a priori estimates are known. Proofs are given by inductive arguments on Gelfand-Shilov semi-norms.

• 出版日期2011