E K Narayanan
Articles written in Proceedings – Mathematical Sciences
Volume 111 Issue 1 February 2001 pp 95-106
We prove an equisummability result for the Fourier expansions and Hermite expansions as well as special Hermite expansions. We also prove the uniform boundedness of the Bochner-Riesz means associated to the Hermite expansions for polyradial functions.
Volume 112 Issue 2 May 2002 pp 321-330
For symmetric spaces of noncompact type we prove an analogue of Hardy’s theorem which characterizes the heat kernel in terms of its order of magnitude and that of its Fourier transform.
Volume 120 Issue 2 April 2010 pp 169-183
We study the Segal–Bargmann transform on $M(2)$. The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer’s type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of $M(2)$. We also prove a Paley–Wiener theorem for the inverse Fourier transform.
Volume 121 Issue 1 February 2011 pp 77-81
We define lacunary Fourier series on a compact connected semisimple Lie group 𝐺. If $f\in L^1(G)$ has lacunary Fourier series and 𝑓 vanishes on a non empty open subset of 𝐺, then we prove that 𝑓 vanishes identically. This result can be viewed as a qualitative uncertainty principle.