Reveals characterizations of Fourier transforms in complex vector bundles, suggesting new theorems for compactly supported distributions.
We study the Fourier transforms for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type X = G/K.We prove a characterization of their range.In fact, from Delorme's Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections.
No takes yet. Share an insight, caveat, or question.
Olbrich et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: