Differential equations and an analog of the Paley-Wiener theorem for linear semisimple Lie groups

DOI10.1017/S0027763000017529zbMath0329.43008OpenAlexW1524014519WikidataQ115336419 ScholiaQ115336419MaRDI QIDQ4095361

Kenneth D. Johnson

Publication date: 1976

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000017529

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Analysis on real and complex Lie groups (22E30) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30) Induced representations for locally compact groups (22D30)

Related Items (5)

Harmonic analysis on reductive Lie groups ⋮ Convexité pour les opérateurs différentiels invariants sur les groupes de Lie ⋮ Invariant differential equations on homogeneous manifolds ⋮ A Paley-Wiener theorem for real reductive groups ⋮ Partial Differential Equations on Semisimple Lie Groups

Cites Work

• Some properties of the Fourier transform on semi-simple Lie groups. I
• Functional analysis on SU(1,1)
• The surjectivity of invariant differential operators on symmetric spaces. I
• An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces
• Discrete series for semisimple Lie groups. II: Explicit determination of the characters
• A duality for symmetric spaces with applications to group representations
• On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups
• Partial Differential Equations on Semisimple Lie Groups

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