Pseudo-Differential Operators on the Affine Group

DOI10.1007/978-3-319-47512-7_1zbMath1377.47018OpenAlexW2585803822MaRDI QIDQ5268872

Aparajita Dasgupta, Man-Wah Wong

Publication date: 21 June 2017

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-47512-7_1

zbMATH Keywords

Fourier transformPlancherel formulapseudo-differential operatorsemi-direct productaffine groupFourier inversion formulaWeyl transform\(\mathrm{SL}(2,\mathbb{R})\)\(L^{2}\)-\(L^p\) estimates

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Pseudodifferential operators (47G30) Analysis on specific locally compact and other abelian groups (43A70)

Related Items (11)

Boundedness and nuclearity of pseudo-differential operators on homogeneous trees ⋮ Characterizations of self-adjointness, normality of pseudo-differential operators on homogeneous space of compact groups ⋮ Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups ⋮ Nuclearity of operators related to finite measure spaces ⋮ Pseudo-differential operators, Wigner transform and Weyl transform on the affine Poincaré group ⋮ Pseudo-differential operators, Wigner transforms and Weyl transforms on the Poincaré unit disk ⋮ Hilbert-schimdt and trace class pseudo-differential operators and Weyl transforms on the affine group ⋮ Schatten class and nuclear pseudo-differential operators on homogeneous spaces of compact groups ⋮ Pseudo-differential operators, Wigner transform and Weyl transform on the similitude group, \(\mathbb{SIM}(2)\) ⋮ Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group ⋮ Boundedness and compactness of localization operators on the affine group

Cites Work

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• A Course in Abstract Harmonic Analysis
• Pseudo-Differential Operators on $$ \mathbb{S}^1 $$
• An Introduction to Pseudo-Differential Operators

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