K. Ramachandran

activity

20122022

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math.CV2022

Conformal Rigidity of Polar Set Complements

Ratna Pal, Koushik Ramachandran, Sivaguru Ravisankar

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

math.CV2019

The closed range property for the $\partial$ -operator on planar domains

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

Let $Ω \subset C$ be an open set. We show that $\partial$ has closed range in $L^{2} (Ω)$ 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 $P_{n}$ of degree $n$ , Bernstein's inequality states that $∥ P_{n}^{'} ∥ \leq n ∥ P_{n} ∥$ for all $L^{p}$ norms on the unit circle, $0 < p \leq \infty,$ with equality for $P_n(z)=…

math.CV2016

Equidistribution of zeros of random polynomials

Igor Pritsker, Koushik Ramachandran

We study the asymptotic distribution of zeros for the random polynomials $P_{n} (z) = \sum_{k = 0}^{n} A_{k} B_{k} (z)$ , where ${A_{k}}_{k = 0}^{\infty}$ are non-trivial i.i.d. complex random va…

Conformal Rigidity of Polar Set Complements

The closed range property for the ∂-operator on planar domains

Random Bernstein-Markov factors

Equidistribution of zeros of random polynomials

The closed range property for the $\partial$ -operator on planar domains