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Назив: G-type spaces of ultradistributions over R+d and the Weyl pseudo-differential operators with radial symbols
Аутори: Jakšić, Smiljana
Pilipović, Stevan 
Prangoski, Bojan
Датум издавања: 1-јул-2017
Часопис: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Сажетак: © 2016, Springer-Verlag Italia. The first part of the paper is devoted to the G-type spaces i.e. the spaces Gαα(R+d), α≥ 1 and their duals which can be described as analogous to the Gelfand-Shilov spaces and their duals but with completely new justification of obtained results. The Laguerre type expansions of the elements in Gαα(R+d), α≥ 1 and their duals characterise these spaces through the exponential and sub-exponential growth of coefficients. We provide the full topological description and by the nuclearity of Gαα(R+d), α≥ 1 the kernel theorem is proved. The second part is devoted to the class of the Weyl operators with radial symbols belonging to the G-type spaces. The continuity properties of this class of pseudo-differential operators over the Gelfand-Shilov type spaces and their duals are proved. In this way the class of the Weyl pseudo-differential operators is extended to the one with the radial symbols with the exponential and sub-exponential growth rate.
URI: https://open.uns.ac.rs/handle/123456789/3143
ISSN: 15787303
DOI: 10.1007/s13398-016-0313-3
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