Around theorems of Ingham-type regarding decay of Fourier transform on R ⁿ , T ⁿ and two step nilpotent Lie groups

Authors

Mithun Bhowmik, Indian Statistical Institute, Kolkata
Swagato K. Ray, Indian Statistical Institute, Kolkata
Suparna Sen, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Bulletin des Sciences Mathematiques

Abstract

Classical results due to Ingham, Levinson 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. We prove some analogues of these results on the n-dimensional Euclidean space, the n-dimensional torus and connected, simply connected two step nilpotent Lie groups. We also use these results to show a unique continuation property of solutions to the initial value problem for time-dependent Schrödinger equations on the Euclidean space and a class of connected, simply connected two step nilpotent Lie groups.

First Page

33

Last Page

73

DOI

10.1016/j.bulsci.2019.02.004

Publication Date

9-1-2019

Recommended Citation

Bhowmik, Mithun; Ray, Swagato K.; and Sen, Suparna, "Around theorems of Ingham-type regarding decay of Fourier transform on R ⁿ , T ⁿ and two step nilpotent Lie groups" (2019). Journal Articles. 730.
https://digitalcommons.isical.ac.in/journal-articles/730