6 papers
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…
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…
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)=…
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…
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…
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,…