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Iswarya Sitiraju

Publications and source records attributed to Iswarya Sitiraju.

5 recordsLinked to original sources
arXiv2026

Analytic Wavefront Sets of Spherical Distributions on De Sitter Space

In this article we determine the wavefront sets of spherical distributions on the de Sitter space dS = G/H, G= SO_{1,n}(R)_e. These are eigendistributions of the Laplacian on dS = G/H invariant under the subgroup H. We construct bases for the spaces of spherical distributions as boundary values of sesquiholomorphic kernels on a certain G-invariant complex domain in dS^n_C containing the de Sitter space as a G-orbit on the boundary. We characterize the elements of the basis by their analytic wavefront sets. We also treat the spherical distributions invariant under O_{1,n-1}(R).

math.FA↗
arXiv2026

$L^r$- Schwartz spaces on split rank one semisimple symmetric spaces

We study the left $K$-invariant $L^r$-Schwartz space and its Fourier transform on split rank one semisimple symmetric spaces $G/H$ for $0<r\leq 2$. We explicitly determine the kernel of the Fourier transform and show that it is spanned by eigenfunctions associated with the discrete spectrum of the Laplace--Beltrami operator on $G/H$.

math.FA↗
arXiv2025

Strichartz estimates for higher order Schrödinger equations with Partial regular initial data

In this paper, we establish refined Strichartz estimates for higher-order Schrödinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev regularity but only regularity with respect to a subset of the spatial variables. As an application of these estimates, we investigate the well-posedness of nonlinear Schrödinger equations with power-type nonlinearities. In addition, we extend our analysis to the Dunkl Schrödinger equations under partial regularity, defined with respect to two distinct root systems. This extension poses significant challenges, mainly due to the lack of a suitable stationary phase method in the Dunkl setting. To overcome this difficulty, we develop a new result that provides an adaptation of the stationary phase method to the framework of Dunkl analysis.

math.AP↗
arXiv2024

Spherical Distributions on the De Sitter Space and their Spectral Singularities

A spherical distribution is an eigendistribution of the Laplace-Beltrami operator with certain invariance on the de Sitter space. Let G'=O(1,n;R) be the Lorentz group and H' = O(1,n-1;R) be its subgroup. The authors Olafsson and Sitiraju have constructed the spherical distributions, which are $H'$-invariant, as boundary values of some sesquiholomorphic kernels. In this survey article we will explore the connections of these kernels with reflection positivity and representations of the group G = SO(1,n;R)_e, which is the connected component of the Lorentz group. We will also discuss the singularities of spherical distributions in terms of their wavefront set.

math.FA↗