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M. G. Nadkarni

Publications and source records attributed to M. G. Nadkarni.

7 recordsLinked to original sources
arXiv2017

A class of Littlewood polynomials that are not $L^α$-flat

We exhibit a class of Littlewood polynomials that are not $L^α$-flat for any $α\geq 0$. Indeed, it is shown that the sequence of Littlewood polynomials is not $L^α$-flat, $α\geq 0$, when the frequency of $-1$ is not in the interval $]\frac14,\frac34[$. We further obtain a generalization of Jensen-Jensen-Hoholdt's result by establishing that the sequence of Littlewood polynomials is not $L^α$-flat for any $α> 2$ if the frequency of $-1$ is not $\frac12$. Finally, we prove that the sequence of palindromic Littlewood polynomials with even degrees are not $L^α$-flat for any $α\geq 0$.

math.NT↗
arXiv2014

Some Notes on Flat Polynomials

Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}} \big(1 +\sum_{j=1}^{N-1} z^{n_j}\big)$ to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat.

math.CV↗
arXiv2013

Calculus of Generalized Riesz Products

In this paper we discuss generalized Riesz products bringing into consideration $H^p$ theory, the notion of Mahler measure, and the zeros of polynomials appearing in the generalized Riesz product. Formula for Radon-Nikodym derivative between two generalized Riesz product is established under suitable conditions. This is then used to formulate a Dichotomy theorem and prove a conditional version of it. A discussion involving flat polynomials is given.

math.DS↗
arXiv2010

On the number of extreme measures with fixed marginals

In this paper we give an improved upper bound, as compared to the one given in [3] for the number of extreme points of the convex set of all G-invariant probability measures on X*Y with given marginals of full support.

math.GM↗