Zobrazeno 1 - 10
of 173
pro vyhledávání: '"Render, H."'
Autor:
Aldaz, J. M., Render, H.
We show that for all homogeneous polynomials $ f_{m}$ of degree $m$, in $d$ variables, and each $j = 1, \dots , d$, we have \begin{equation*} \left\langle x_{j}^{2}f_{m},f_{m}\right\rangle _{L^{2}\left( \mathbb{S}% ^{d-1}\right) } \geq \frac{\pi ^{2}
Externí odkaz:
http://arxiv.org/abs/2404.16735
We consider inequalities of Bombieri type for polynomials that need not be homogeneous, using the apolar inner product.
Comment: 9 pp
Comment: 9 pp
Externí odkaz:
http://arxiv.org/abs/2403.10584
Autor:
Aldaz, J. M., Render, H.
The existence of decompositions of the form $f=P\cdot q+r$ with $P_k^{\ast}\left( D\right) r=0 $, where $f$ is entire, $P$ a polynomial and $P^{\ast}_k$ the principal part of $P$ with its coefficients conjugated, was achieved in \cite{AlRe23} under c
Externí odkaz:
http://arxiv.org/abs/2403.10419
Autor:
Aldaz, J. M., Render, H.
Publikováno v:
Analysis and Mathematical Physics (2023) 13:91
We continue the study initiated by H. S. Shapiro on Fischer decompositions of entire functions, showing that such decomposition exist in a weak sense (we do not prove uniqueness) under hypotheses regarding the order of the entire function $f$ to be e
Externí odkaz:
http://arxiv.org/abs/2403.10400
Autor:
Aldaz, J. M., Render, H.
Let $P$ be a fixed homogeneous polynomial. We present a sharp condition on $P$ guaranteeing the existence of asymptotically larger bounds in Bombieri's inequality, so for every homogeneous polynomial $q_m$ of degree $m$ we have \begin{equation*} \lef
Externí odkaz:
http://arxiv.org/abs/2402.19153
Autor:
Render, H., Aldaz, J. M.
Let $P_{2k}$ be a homogeneous polynomial of degree $2k$ and assume that there exist $C>0$, $D>0$ and $\alpha \ge 0$ such that \begin{equation*} \left\langle P_{2k}f_{m},f_{m}\right\rangle_{L^2(\mathbb{S}^{d-1})}\geq \frac{1}{C\left( m+D\right) ^{\alp
Externí odkaz:
http://arxiv.org/abs/2209.03134
Autor:
Aldaz, J. M., Render, H.
We study certain generalizations of the classical Bernstein operators, defined via increasing sequences of nodes. Such operators are required to fix two functions, $f_0$ and $f_1$, such that $f_0 > 0$ and $f_1/ f_0$ is increasing on an interval $[a,b
Externí odkaz:
http://arxiv.org/abs/1803.05343
Autor:
Aldaz, J. M., Render, H.
Publikováno v:
Mediterr. J. Math. 15 (2018), no. 6, 15:222
We study generalizations of the classical Bernstein operators on polynomial spaces, where instead of fixing $\mathbf{1}$ and $x$, we require that $\mathbf{1}$ and a strictly increasing polynomial $f_1$ be fixed. Via several examples, we exhibit the d
Externí odkaz:
http://arxiv.org/abs/1803.01673
Autor:
Kounchev, O., Render, H.
Publikováno v:
In Journal of Computational and Applied Mathematics 1 August 2021 391
Autor:
Kounchev, O., Render, H.
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier series of the weight function and a reduction of the bivariate integral i
Externí odkaz:
http://arxiv.org/abs/1509.00283