• E K Narayanan

Articles written in Proceedings – Mathematical Sciences

• On the equisummability of Hermite and Fourier expansions

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.

• The heat kernel and Hardy’s theorem on symmetric spaces of noncompact type

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.

• Segal-Bargmann Transform and Paley-Wiener Theorems on $M(2)$

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.

• Lacunary Fourier Series and a Qualitative Uncertainty Principle for Compact Lie Groups

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.

• Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
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• Editorial Note on Continuous Article Publication

Posted on July 25, 2019