TY  - CHAP
AU  - Jakšić, Smiljana
AU  - Pilipović, S.
PY  - 2024
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/1473
AB  - In this paper we introduce classes of ultradifferentiable functions and the corresponding ultradistributions on ℝ+d, i.e. Gαβ(ℝ+d) and (Gαβ(ℝ+d))′, α,β gt 0, respectively. We give their characterisation through the Laguerre coefficients estimate. Furthermore, we define the modified fractional power of the partial Hankel-Clifford transform and show that this transformation is a topological isomorphism on Gαα(ℝ+d), α≥1. We also investigate the boundedness of the Weyl pseudo-differential operators with symbols from the previously introduced spaces.
PB  - Springer Science and Business Media Deutschland GmbH
T2  - Trends in Mathematics
T1  - The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators
EP  - 207
SP  - 197
VL  - 5
DO  - 10.1007/978-3-031-57005-6_21
UR  - conv_1863
ER  - 

@inbook{
author = "Jakšić, Smiljana and Pilipović, S.",
year = "2024",
abstract = "In this paper we introduce classes of ultradifferentiable functions and the corresponding ultradistributions on ℝ+d, i.e. Gαβ(ℝ+d) and (Gαβ(ℝ+d))′, α,β gt 0, respectively. We give their characterisation through the Laguerre coefficients estimate. Furthermore, we define the modified fractional power of the partial Hankel-Clifford transform and show that this transformation is a topological isomorphism on Gαα(ℝ+d), α≥1. We also investigate the boundedness of the Weyl pseudo-differential operators with symbols from the previously introduced spaces.",
publisher = "Springer Science and Business Media Deutschland GmbH",
journal = "Trends in Mathematics",
booktitle = "The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators",
pages = "207-197",
volume = "5",
doi = "10.1007/978-3-031-57005-6_21",
url = "conv_1863"
}

Jakšić, S.,& Pilipović, S.. (2024). The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators. in Trends in Mathematics
Springer Science and Business Media Deutschland GmbH., 5, 197-207.
https://doi.org/10.1007/978-3-031-57005-6_21
conv_1863

Jakšić S, Pilipović S. The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators. in Trends in Mathematics. 2024;5:197-207.
doi:10.1007/978-3-031-57005-6_21
conv_1863 .

Jakšić, Smiljana, Pilipović, S., "The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators" in Trends in Mathematics, 5 (2024):197-207,
https://doi.org/10.1007/978-3-031-57005-6_21 .,
conv_1863 .

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 .

TY  - JOUR
AU  - Jakšić, Smiljana
AU  - Pilipović, Stevan
PY  - 2023
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/1386
AB  - We investigate various G type spaces on Rd+ and their relations with the Gelfand-Shilov S type spaces on R2d through the mapping w : R2d-* Rd+, w(x, & xi;) = (2x21 + 2 & xi;21, ... , 2x2d + 2 & xi;2d). 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.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - ψDOs with radial symbols and spaces of type G
EP  - 8763
IS  - 26
SP  - 8755
VL  - 37
DO  - 10.2298/FIL2326755J
UR  - conv_1718
ER  - 

@article{
author = "Jakšić, Smiljana and Pilipović, Stevan",
year = "2023",
abstract = "We investigate various G type spaces on Rd+ and their relations with the Gelfand-Shilov S type spaces on R2d through the mapping w : R2d-* Rd+, w(x, & xi;) = (2x21 + 2 & xi;21, ... , 2x2d + 2 & xi;2d). 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.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "ψDOs with radial symbols and spaces of type G",
pages = "8763-8755",
number = "26",
volume = "37",
doi = "10.2298/FIL2326755J",
url = "conv_1718"
}

Jakšić, S.,& Pilipović, S.. (2023). ψDOs with radial symbols and spaces of type G. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 37(26), 8755-8763.
https://doi.org/10.2298/FIL2326755J
conv_1718

Jakšić S, Pilipović S. ψDOs with radial symbols and spaces of type G. in Filomat. 2023;37(26):8755-8763.
doi:10.2298/FIL2326755J
conv_1718 .

Jakšić, Smiljana, Pilipović, Stevan, "ψDOs with radial symbols and spaces of type G" in Filomat, 37, no. 26 (2023):8755-8763,
https://doi.org/10.2298/FIL2326755J .,
conv_1718 .

TY  - JOUR
AU  - Jakšić, Smiljana
AU  - Maksimović, Snjezana
AU  - Pilipović, Stevan
PY  - 2018
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/920
AB  - We construct the space of pseudo-quotients that is shown to be isomorphic to the spaces of Beurling tempered ultradistributions.
T2  - Journal of Mathematical Analysis and Applications
T1  - An algebraic approach to tempered ultradistributions
EP  - 935
IS  - 1
SP  - 927
VL  - 466
DO  - 10.1016/j.jmaa.2018.06.033
UR  - conv_1355
ER  - 

@article{
author = "Jakšić, Smiljana and Maksimović, Snjezana and Pilipović, Stevan",
year = "2018",
abstract = "We construct the space of pseudo-quotients that is shown to be isomorphic to the spaces of Beurling tempered ultradistributions.",
journal = "Journal of Mathematical Analysis and Applications",
title = "An algebraic approach to tempered ultradistributions",
pages = "935-927",
number = "1",
volume = "466",
doi = "10.1016/j.jmaa.2018.06.033",
url = "conv_1355"
}

Jakšić, S., Maksimović, S.,& Pilipović, S.. (2018). An algebraic approach to tempered ultradistributions. in Journal of Mathematical Analysis and Applications, 466(1), 927-935.
https://doi.org/10.1016/j.jmaa.2018.06.033
conv_1355

Jakšić S, Maksimović S, Pilipović S. An algebraic approach to tempered ultradistributions. in Journal of Mathematical Analysis and Applications. 2018;466(1):927-935.
doi:10.1016/j.jmaa.2018.06.033
conv_1355 .

Jakšić, Smiljana, Maksimović, Snjezana, Pilipović, Stevan, "An algebraic approach to tempered ultradistributions" in Journal of Mathematical Analysis and Applications, 466, no. 1 (2018):927-935,
https://doi.org/10.1016/j.jmaa.2018.06.033 .,
conv_1355 .

TY  - JOUR
AU  - Jakšić, Smiljana
AU  - Pilipović, Stevan
AU  - Prangoski, Bojan
PY  - 2017
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/825
AB  - The first part of the paper is devoted to the G-type spaces i.e. the spaces G(alpha)(alpha)(R-+(d)), alpha  gt = 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 G(alpha)(alpha) (R-+(d)), alpha  gt = 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 G(alpha)(alpha)(R-+(d)), alpha  gt = 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.
T2  - Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas
T1  - G -type spaces of ultradistributions over R + d and the Weyl pseudo-differential operators with radial symbols
EP  - 640
IS  - 3
SP  - 613
VL  - 111
DO  - 10.1007/s13398-016-0313-3
UR  - conv_1273
ER  - 

@article{
author = "Jakšić, Smiljana and Pilipović, Stevan and Prangoski, Bojan",
year = "2017",
abstract = "The first part of the paper is devoted to the G-type spaces i.e. the spaces G(alpha)(alpha)(R-+(d)), alpha  gt = 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 G(alpha)(alpha) (R-+(d)), alpha  gt = 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 G(alpha)(alpha)(R-+(d)), alpha  gt = 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.",
journal = "Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas",
title = "G -type spaces of ultradistributions over R + d and the Weyl pseudo-differential operators with radial symbols",
pages = "640-613",
number = "3",
volume = "111",
doi = "10.1007/s13398-016-0313-3",
url = "conv_1273"
}

Jakšić, S., Pilipović, S.,& Prangoski, B.. (2017). G -type spaces of ultradistributions over R + d and the Weyl pseudo-differential operators with radial symbols. in Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas, 111(3), 613-640.
https://doi.org/10.1007/s13398-016-0313-3
conv_1273

Jakšić S, Pilipović S, Prangoski B. G -type spaces of ultradistributions over R + d and the Weyl pseudo-differential operators with radial symbols. in Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas. 2017;111(3):613-640.
doi:10.1007/s13398-016-0313-3
conv_1273 .

Jakšić, Smiljana, Pilipović, Stevan, Prangoski, Bojan, "G -type spaces of ultradistributions over R + d and the Weyl pseudo-differential operators with radial symbols" in Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas, 111, no. 3 (2017):613-640,
https://doi.org/10.1007/s13398-016-0313-3 .,
conv_1273 .

TY  - JOUR
AU  - Jakšić, Smiljana
AU  - Maksimović, Snjezana
AU  - Pilipović, Stevan
AU  - Prangoski, Bojan
PY  - 2017
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/814
AB  - The aim of this paper is twofold. Firstly, to show the existence of topological isomorphism between the G-type spaces G(alpha)(alpha) (R-+(d)), alpha  gt = 1 and the subspaces of the Gelfand-Shilov spaces S-alpha/2 (alpha/2) (Rd), alpha  gt = 1, consisting of "even" functions. The same is done for their dual spaces. Secondly, to obtain two structural theorems for the dual spaces (G(alpha)(alpha)(R-+(d)))', alpha  gt = 1.
T2  - Journal of Pseudo-Differential Operators and Applications
T1  - Relations between Hermite and Laguerre expansions of ultradistributions over R d and R + d
EP  - 296
IS  - 2
SP  - 275
VL  - 8
DO  - 10.1007/s11868-016-0171-y
UR  - conv_1268
ER  - 

@article{
author = "Jakšić, Smiljana and Maksimović, Snjezana and Pilipović, Stevan and Prangoski, Bojan",
year = "2017",
abstract = "The aim of this paper is twofold. Firstly, to show the existence of topological isomorphism between the G-type spaces G(alpha)(alpha) (R-+(d)), alpha  gt = 1 and the subspaces of the Gelfand-Shilov spaces S-alpha/2 (alpha/2) (Rd), alpha  gt = 1, consisting of "even" functions. The same is done for their dual spaces. Secondly, to obtain two structural theorems for the dual spaces (G(alpha)(alpha)(R-+(d)))', alpha  gt = 1.",
journal = "Journal of Pseudo-Differential Operators and Applications",
title = "Relations between Hermite and Laguerre expansions of ultradistributions over R d and R + d",
pages = "296-275",
number = "2",
volume = "8",
doi = "10.1007/s11868-016-0171-y",
url = "conv_1268"
}

Jakšić, S., Maksimović, S., Pilipović, S.,& Prangoski, B.. (2017). Relations between Hermite and Laguerre expansions of ultradistributions over R d and R + d. in Journal of Pseudo-Differential Operators and Applications, 8(2), 275-296.
https://doi.org/10.1007/s11868-016-0171-y
conv_1268

Jakšić S, Maksimović S, Pilipović S, Prangoski B. Relations between Hermite and Laguerre expansions of ultradistributions over R d and R + d. in Journal of Pseudo-Differential Operators and Applications. 2017;8(2):275-296.
doi:10.1007/s11868-016-0171-y
conv_1268 .

Jakšić, Smiljana, Maksimović, Snjezana, Pilipović, Stevan, Prangoski, Bojan, "Relations between Hermite and Laguerre expansions of ultradistributions over R d and R + d" in Journal of Pseudo-Differential Operators and Applications, 8, no. 2 (2017):275-296,
https://doi.org/10.1007/s11868-016-0171-y .,
conv_1268 .