Symmetric spaces; Fourier transform; Linear invariant differential equations
Abstract :
[en] We study the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type. We show how this can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander’s proof of the Ehrenpreis-Malgrange theorem. We get complete solvability for the hyperbolic plane H2 and partial results for finite products H2 × · · · × H2 and the hyperbolic 3-space H3. [lb] Mir studéieren Fourier Transformatioun fir Distributiounal Sektiounen vu Vektorbündelen u symmetresch Réim vun engem net-kompakten Typ. Mir bewéisen wéi et fir d’Léisbarkeet vu Systémer vun invarianten Differentialequatiounen an Analogie zu Hörmander’s Schätzungen, ugewand ka ginn. Mir kréien komplett Léisbarkeet fir hyperbolesch Pléng H2 a partial Résultater fir Produkter H2 ×· · ·×H2, wéi och fir hyperbolesch 3-Réim H3.
Research center :
Department of Mathematics
Disciplines :
Mathematics
Author, co-author :
Palmirotta, Guendalina ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
English
Title :
Solvability of systems of invariant differential equations on symmetric spaces G/K
