activity
20122022
collaborators

6 papers

math.CV2022

Conformal Rigidity of Polar Set Complements

Ratna Pal, Koushik Ramachandran, Sivaguru Ravisankar

Let be a closed polar subset of . In this short note, we use elementary potential theoretic tools to show that any conformal map on is nece…

math.CV2019

The closed range property for the -operator on planar domains

A. -K. Gallagher, J. Lebl, K. Ramachandran

Let be an open set. We show that has closed range in if and only if the Poincaré-Dirichlet inequality holds. Moreover, we give…

math.CV2018

Random Bernstein-Markov factors

Igor Pritsker, Koushik Ramachandran

For a polynomial of degree , Bernstein's inequality states that for all norms on the unit circle, with equality for $P_n(z)=…

math.PR2017

Natural boundary and zero distribution of random polynomials in smooth domains

Igor Pritsker, Koushik Ramachandran

We consider the zero distribution of random polynomials of the form , where are non-trivial i.i.d. complex random variabl…

math.CV2016

Equidistribution of zeros of random polynomials

Igor Pritsker, Koushik Ramachandran

We study the asymptotic distribution of zeros for the random polynomials , where are non-trivial i.i.d. complex random va…

math.AP2012

Asymptotic behavior of positive harmonic functions in certain unbounded domains

Koushik Ramachandran

We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling,…