Uncertainty Principles of Ingham and Paley-Wiener on Semisimple Lie Groups

2016/06/07 by Mithun Bhowmik, Bhowmik, Mithun, Suparna Sen +1
Mathematics · #Advanced Mathematical Physics Problems #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1606.02125

openalex publication_date 2016/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Classical results due to Ingham and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. Viewing these results as uncertainty principles for Fourier transforms, we prove certain analogues of these results on connected, noncompact, semisimple Lie groups with finite center. We also use these results to show unique continuation property of solutions to the initial value problem for time-dependent Schrödinger equations on Riemmanian symmetric spaces of noncompact type.

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