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Solvability of invariant systems of differential equations on the hyperbolic plane
Palmirotta, Guendalina


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Abstract :
[en] In the Euclidean case, it is well-known, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this situation and consider systems of linear invariant differential operators, is still solvable? In case of Rn (for some positive integer n), the question has been proved mainly by Hörmander. We will show that this remains still true for Riemannian symmetric spaces of non-compact type X = G/K. More precisely, we will present a possible strategy to solve this problem by using the Fourier trans- form and its Paley-Wiener(-Schwartz) theorem for (distributional) sections of vector bundles over X. We will get complete solvability for the hyperbolic plane H2 = SL(2, R)/SO(2) and beyond. This work was part of my doctoral dissertation supervised by Martin Olbrich.
Disciplines :
Author, co-author :
Palmirotta, Guendalina  ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
Title :
Solvability of invariant systems of differential equations on the hyperbolic plane
Publication date :
28 June 2022
Event name :
Oberseminar "Geometrische Analysis und Zahlentheorie"
Event organizer :
Christian Arends and Jan Frahm
Event place :
Paderborn, Germany
Event date :
Audience :
Name of the research project :
Funders :
FNR - Fonds National de la Recherche [LU]
Available on ORBilu :
since 04 June 2022


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