TY  - JOUR
AU  - Jakšić, Smiljana
AU  - Pilipović, Stevan
AU  - Prangoski, Bojan
PY  - 2023
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/1413
AB  - We analyse a class of pseudo-differential operators in the Gelfand-Shilov setting whose Weyl symbols are radial in each phase-space variable separately. Namely, the symbols are of the forma(& thetasym;)(x,xi) := a(2x(1)(2) + 2 xi(2)(1), . . ., 2x(d)(2) + 2 xi(2)(d)),where a is a measurable function on R-+(d):= {r is an element of R-d | r(j) gt  0, j = 1, ... , d} and has Gelfand-Shilov L-p-growths. We prove that the action of these pseudo-differential operators on a Gelfand-Shilov ultradistribution f can be given by a series of Her-mite functions with coefficients that are explicitly computed in terms of the Laguerre coefficients of a and the Hermite coefficients of f . As a consequence, we give a characterisation of the functions a in terms of the growths of their Laguerre coefficients for which the Weyl quantisation of a(& thetasym;) are globally Gelfand-Shilov regular.
T2  - Journal of Pseudo-Differential Operators and Applications
T1  - Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable
IS  - 1
VL  - 14
DO  - 10.1007/s11868-023-00505-x
UR  - conv_1681
ER  - 

@article{
author = "Jakšić, Smiljana and Pilipović, Stevan and Prangoski, Bojan",
year = "2023",
abstract = "We analyse a class of pseudo-differential operators in the Gelfand-Shilov setting whose Weyl symbols are radial in each phase-space variable separately. Namely, the symbols are of the forma(& thetasym;)(x,xi) := a(2x(1)(2) + 2 xi(2)(1), . . ., 2x(d)(2) + 2 xi(2)(d)),where a is a measurable function on R-+(d):= {r is an element of R-d | r(j) gt  0, j = 1, ... , d} and has Gelfand-Shilov L-p-growths. We prove that the action of these pseudo-differential operators on a Gelfand-Shilov ultradistribution f can be given by a series of Her-mite functions with coefficients that are explicitly computed in terms of the Laguerre coefficients of a and the Hermite coefficients of f . As a consequence, we give a characterisation of the functions a in terms of the growths of their Laguerre coefficients for which the Weyl quantisation of a(& thetasym;) are globally Gelfand-Shilov regular.",
journal = "Journal of Pseudo-Differential Operators and Applications",
title = "Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable",
number = "1",
volume = "14",
doi = "10.1007/s11868-023-00505-x",
url = "conv_1681"
}

Jakšić, S., Pilipović, S.,& Prangoski, B.. (2023). Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable. in Journal of Pseudo-Differential Operators and Applications, 14(1).
https://doi.org/10.1007/s11868-023-00505-x
conv_1681

Jakšić S, Pilipović S, Prangoski B. Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable. in Journal of Pseudo-Differential Operators and Applications. 2023;14(1).
doi:10.1007/s11868-023-00505-x
conv_1681 .

Jakšić, Smiljana, Pilipović, Stevan, Prangoski, Bojan, "Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable" in Journal of Pseudo-Differential Operators and Applications, 14, no. 1 (2023),
https://doi.org/10.1007/s11868-023-00505-x .,
conv_1681 .