Geodesic
Ψdos with radial symbols and spaces of type G
Filomat, Tome 37 (2023) no. 26, p. 8755

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DOI

We investigate various G type spaces on R d + and their relations with the Gelfand-Shilov S type spaces on R 2d through the mapping w : R 2d → R d + , w(x, ξ) = (2x 2 1 + 2ξ 2 1 ,. .. , 2x 2 d + 2ξ 2 d). Sufficient conditions for the hypoellipticity of symbols originating from the coordinante radial symbols in G type spaces are also given. Two open problems explained in the introduction are posed.
DOI : 10.2298/FIL2326755J
Classification : 47G30, 46F12, 33C45, 44A15, 35S05
Keywords: Pseudo-differential operators with radial symbols, Gelfand-Shilov regularity, Hermite expansions, Laguerre expansions 
Smiljana Jakšić; Stevan Pilipović. Ψdos with radial symbols and spaces of type G. Filomat, Tome 37 (2023) no. 26, p. 8755 . doi: 10.2298/FIL2326755J
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     author = {Smiljana Jak\v{s}i\'c and Stevan Pilipovi\'c},
     title = {\ensuremath{\Psi}dos with radial symbols and spaces of type {G}},
     journal = {Filomat},
     pages = {8755 },
     year = {2023},
     volume = {37},
     number = {26},
     doi = {10.2298/FIL2326755J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2326755J/}
}
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