Hilbert-Schimdt and Trace Class Pseudo-Differential Operators and Weyl Transforms on the Affine Group

被引：4

作者：

Dasgupta, Aparajita ^{[1
]}

Nayak, Santosh Kumar ^{[1
]}

Wong, M. W. ^{[2
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

[2] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2021年 / 12卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Affine group; Duflo-Moore operators; Fourier transform; Hilbert-Schimdt operator; Trace class operator; Trace; Fourier-Wigner transform; Wigner transform; Weyl transform; Primary; 47G30;

D O I：

10.1007/s11868-021-00380-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give necessary and sufficient conditions on the symbols for which the corresponding pseudo-differential operators on the affine group are Hilbert-Schimdt operators. We also give a characterization of trace class pseudo-differential operators on the affine group. A trace formula for these trace class operators is also obtained. We have also obtained the L2 boundedness of the Weyl transforms on the affine group.

引用

页数：19

共 12 条

[1] Hilbert–Schimdt and Trace Class Pseudo-Differential Operators and Weyl Transforms on the Affine Group
Aparajita Dasgupta
Santosh Kumar Nayak
M. W. Wong
Journal of Pseudo-Differential Operators and Applications, 2021, 12
[2] Pseudo-differential Operators, Wigner Transforms and Weyl Transforms on the Poincar, Unit Disk
Molahajloo, Shahla
COMPLEX ANALYSIS AND OPERATOR THEORY, 2018, 12 (03) : 811 - 833
[3] Pseudo-differential Operators, Wigner Transforms and Weyl Transforms on the Poincaré Unit Disk
Shahla Molahajloo
Complex Analysis and Operator Theory, 2018, 12 : 811 - 833
[4] Hilbert–Schmidt and trace class pseudo-differential operators on the Heisenberg group
Aparajita Dasgupta
M. W. Wong
Journal of Pseudo-Differential Operators and Applications, 2013, 4 : 345 - 359
[5] Hilbert-Schmidt and trace class pseudo-differential operators on the Heisenberg group
Dasgupta, Aparajita
Wong, M. W.
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2013, 4 (03) : 345 - 359
[6] Pseudo-differential operators, Wigner transform and Weyl transform on the affine Poincare group
Dasgupta, Aparajita
Nayak, Santosh Kumar
BULLETIN DES SCIENCES MATHEMATIQUES, 2023, 184
[7] MAXIMAL COVARIANCE GROUP OF WIGNER TRANSFORMS AND PSEUDO-DIFFERENTIAL OPERATORS
Dias, Nuno Costa
de Gosson, Maurice A.
Prata, Joao Nuno
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (09) : 3183 - 3192
[8] Weyl Rule and Pseudo-Differential Operators for Arbitrary Operators
Cohen, Leon
PSEUDO-DIFFERENTIAL OPERATORS: ANALYSIS, APPLICATIONS AND COMPUTATIONS, 2011, 213 : 251 - 264
[9] C*-algebras, H*-algebras and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups
Kumar, Vishvesh
Wong, M. W.
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2019, 10 (02) : 269 - 283
[10] A New Class of Pseudo-Differential Operators Involving Linear Canonical Transform
Kumar M.
International Journal of Applied and Computational Mathematics, 2020, 6 (6)

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