Zobrazeno 1 - 10
of 19
pro vyhledávání: '"11C08, 41A17"'
Autor:
Erdélyi, Tamás
Littlewood polynomials are polynomials with each of their coefficients in $\{-1,1\}$. A sequence of Littlewood polynomials that satisfies a remarkable flatness property on the unit circle of the complex plane is given by the Rudin-Shapiro polynomials
Externí odkaz:
http://arxiv.org/abs/2311.04395
Autor:
Erdélyi, Tamás
Let either $R_k(t) := |P_k(e^{it})|^2$ or $R_k(t) := |Q_k(e^{it})|^2$, where $P_k$ and $Q_k$ are the usual Rudin-Shapiro polynomials of degree $n-1$ with $n=2^k$. The graphs of $R_k$ on the period suggest many zeros of $R_k(t)-n$ in a dense fashion o
Externí odkaz:
http://arxiv.org/abs/2210.04385
In a celebrated paper, Borwein, Erd\'elyi, Ferguson and Lockhart constructed cosine polynomials of the form \[ f_A(x) = \sum_{a \in A} \cos(ax), \] with $A\subseteq \mathbb{N}$, $|A|= n$ and as few as $n^{5/6+o(1)}$ zeros in $[0,2\pi]$, thereby dispr
Externí odkaz:
http://arxiv.org/abs/2005.01695
Autor:
Erdélyi, Tamás
Polynomials with coefficients in $\{-1,1\}$ are called Littlewood polynomials. Using special properties of the Rudin-Shapiro polynomials and classical results in approximation theory such as Jackson's Theorem, de la Vall\'ee Poussin sums, Bernstein's
Externí odkaz:
http://arxiv.org/abs/2001.08151
Autor:
Erdélyi, Tamás
Let $${\mathcal K}_n := \left\{p_n: p_n(z) = \sum_{k=0}^n{a_k z^k}, \enspace a_k \in {\mathbb C}\,,\enspace |a_k| = 1 \right\}\,.$$ A sequence $(P_n)$ of polynomials $P_n \in {\mathcal K}_n$ is called ultraflat if $(n + 1)^{-1/2}|P_n(e^{it})|$ conver
Externí odkaz:
http://arxiv.org/abs/1810.04287
Autor:
Erdélyi, Tamás
Let either $R_k(t) := |P_k(e^{it})|^2$ or $R_k(t) := |Q_k(e^{it})|^2$, where $P_k$ and $Q_k$ are the usual Rudin-Shapiro polynomials of degree $n-1$ with $n=2^k$. In a recent paper we combined close to sharp upper bounds for the modulus of the autoco
Externí odkaz:
http://arxiv.org/abs/1802.02906
Autor:
Erdélyi, Tamás
In signal processing the Rudin-Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. Binary sequences with low autocorrelation coefficients are of interest in radar, sonar, and communication systems.
Externí odkaz:
http://arxiv.org/abs/1708.01189
Autor:
Sahasrabudhe, Julian
We show that if $A$ is a finite set of non-negative integers then the number of zeros of the function \[ f_A(\theta) = \sum_{a \in A} \cos(a\theta), \] in $[0,2\pi]$, is at least $(\log \log \log |A|)^{1/2-\varepsilon}$. This gives the first uncondit
Externí odkaz:
http://arxiv.org/abs/1610.07680
Autor:
Erdelyi, Tamas
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
Externí odkaz:
http://arxiv.org/abs/1602.02315
Autor:
Erdelyi, Tamas
We study the number of real zeros of trigonometric polynomials in a period and the number of zeros of self-reciprocal algebraic polynomials on the unit circle under the assumption that their coefficients are in a fixed finite set of real numbers.
Externí odkaz:
http://arxiv.org/abs/1602.02284