Suresh Eswarathasan

activity

20102024

most citedAveraged Pointwise Bounds for Deformations of Schrodinger Eigenfunctions

6 citations · 6 across the 10 of their papers we have counts for

collaborators

18 papers

math.AP2024

Pointwise Weyl Laws for Quantum Completely Integrable Systems

Suresh Eswarathasan, Allan Greenleaf, Blake Keeler

The study of the asymptotics of the spectral function for self-adjoint, elliptic differential, or more generally pseudodifferential, operators on a compact manifold has a long hist…

math.AP2023

Nodal sets of eigenfunctions of sub-Laplacians

Suresh Eswarathasan, Cyril Letrouit

Nodal sets of eigenfunctions of elliptic operators on compact manifolds have been studied extensively over the past decades. In this note, we initiate the study of nodal sets of ei…

math.CA2021

Fractal uncertainty principle for discrete Cantor sets with random alphabets

Suresh Eswarathasan, Xiaolong Han

In this paper, we investigate the fractal uncertainty principle (FUP) for discrete Cantor sets, which are determined by an alphabet from a base of digits. Consider the base of M di…

math.SP2021

Laplace-Beltrami spectrum of ellipsoids that are close to spheres and analytic perturbation theory

Suresh Eswarathasan, Theodore Kolokolnikov

We study the spectrum of the Laplace-Beltrami operator on ellipsoids. For ellipsoids that are close to the sphere, we use analytic perturbation theory to estimate the eigenvalues u…

math.SP2021

Entropy of logarithmic modes

Suresh Eswarathasan

Let $(M, g)$ be a compact, boundaryless, Riemannian manifold whose geodesic flow on its unit sphere bundle is Anosov. Consider the (semiclassical) Laplace-Beltrami operator on $M$ .…

math.PR2020

Effective bounds for monochromatic connectivity measures in two dimensions

Matthew de Courcy-Ireland, Suresh Eswarathasan

We establish numerical lower bounds for the monochromatic connectivity measure in two dimensions introduced by Sarnak and Wigman. This measure dictates among the nodal domains of a…

math.PR2019

Direction distribution for nodal components of random band-limited functions on surfaces

Suresh Eswarathasan, Igor Wigman

Let $(M, g)$ be a smooth compact Riemannian surface with no boundary. Given a smooth vector field $V$ with finitely many zeroes on $M$ , we study the distribution of the number of ta…

math.AP2019

Restriction of Laplace-Beltrami eigenfunctions to arbitrary sets on manifolds

Suresh Eswarathasan, Malabika Pramanik

Given a compact Riemannian manifold $(M, g)$ without boundary, we estimate the Lebesgue norm of Laplace-Beltrami eigenfunctions when restricted to a wide variety of subsets $Γ$ of…

math.SP2018

Tangent nodal sets for random spherical harmonics

Suresh Eswarathasan

In this note, we consider a fixed vector field $V$ on $S^{2}$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ is also tange…

math.AP2016

Scarring of quasimodes on hyperbolic manifolds

Suresh Eswarathasan, Lior Silberman

Let $N$ be a compact hyperbolic manifold, $M \subset N$ an embedded totally geodesic submanifold, and let $- ℏ^{2} Δ_{N}$ be the semiclassical Laplace--Beltrami operator. For any $\…

math.AP2015

Strong Scarring of Logarithmic Quasimodes

Suresh Eswarathasan, Stéphane Nonnenmacher

We consider a semiclassical (pseudo)differential operator on a compact surface $(M, g)$ , such that the Hamiltonian flow generated by its principal symbol admits a hyperbolic periodi…

math.AP2014

Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces

Suresh Eswarathasan, Gabriel Riviere

We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at…

math.AP2014

Expected values of eigenfunction periods

Suresh Eswarathasan

Let $(M, g)$ be a compact Riemannian surface. Consider a family of $L^{2}$ normalized Laplace-Beltrami eigenfunctions, written in the semiclassical form $- h_{j}^{2} Δ_{g} ϕ_{h_{j}} = ϕ_{h_{j}}$ ,…

math.CA2013

Intersections of sets, diophantine equations and Fourier analysis

Suresh Eswarathasan, Alex Iosevich, Krystal Taylor

A classical theorem due to Mattila (see \cite{Mat84}; see also \cite{M95}, Chapter 13) says that if $A, B \subset R^{d}$ of Hausdorff dimension $s_{A}, s_{B}$ , respectively, with $…

math.AP2013

Smooth billiards with a large Weyl remainder

Suresh Eswarathasan, Iosif Polterovich, John A. Toth

The celebrated Hardy-Landau lower bound for the error term in the Gauss's circle problem can be viewed as an estimate from below for the remainder in Weyl's law on a square, with e…

math.SP2011★ 6 cited

Averaged Pointwise Bounds for Deformations of Schrodinger Eigenfunctions

Suresh Eswarathasan, John A. Toth

Let (M,g) be a n-dimensional compact Riemannian manifold. We consider the magnetic deformations of semiclassical Schrodinger operators on M for a family of magnetic potentials that…

math.AP2011

Microlocal analysis of scattering data for nested conormal potentials

Suresh Eswarathasan

Working in the time domain, we show that the location of the singularities and the principal symbol of a potential that is conormal to nested submanifolds $S_2 \subset S_1 \subset…

math.CA2010

Fourier integral operators, fractal sets and the regular value theorem

Suresh Eswarathasan, Alex Iosevich, Krystal Taylor

We prove that if $E \subset R^{2 d}$ , $d \geq 2$ , is an Ahlfors-David regular product set of sufficiently large Hausdorff dimension, denoted by $dim_{\mathcal H}({\…