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 P-Adic Numbers Ultrametric Anal. Appl., 2012, Volume 4, Number 1, Pages 64–75 (Mi padic10)

Homogeneous generalized functions with respect to one-parametric group

Yu. N. Drozhzhinova, B. I. Zavialov

a Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, Moscow 119991, Russia

Abstract: We give the full description of homogeneous generalized functions along the trajectories of arbitrary one-parametric multiplicative group of linear transformations whose generator matrix has eigenvalues with positive real parts. We also study the problem of extension of such functionals from the space of test functions vanishing at the origin up to the whole space $S(\mathbb{R}^n)$, and discuss the conditions of uniqueness of such extension.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation NSH 2928.2012.1 Russian Foundation for Basic Research 10-01-00178 Work on this paper was supported by RFBR, grant 10-01-00178, and RF NSH 2928.2012.1.

DOI: https://doi.org/10.1134/S2070046612010086

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Document Type: Article