J. M. Aldaz

most citedA Fischer type decomposition theorem from the apolar inner product

3 citations · 3 across the 3 of their papers we have counts for

collaborators

6 papers

math.CA2026

There is no degree independent Bombieri type inequality for non-homogeneous polynomials

J. M. Aldaz

Bombieri's inequality for polynomials requires that at least one of them be homogeneous. In this note an AI provides a natural example showing that, as stated in the title, there i…

math.AP2024

The Dirichlet problem with entire data for non-hyperbolic quadratic hypersurfaces

J. M. Aldaz, H. Render

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}\righ…

math.CA2024

The apolar inner product and a Bombieri type inequality for polynomials

J. M. Aldaz, A. Bravo, H. Render

We consider inequalities of Bombieri type for polynomials that need not be homogeneous, using the apolar inner product.

math.AP2024★ 3 cited

A Fischer type decomposition theorem from the apolar inner product

J. M. Aldaz, H. Render

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) u…

math.AP2024

Fischer decompositions for entire functions of sufficiently low order

J. M. Aldaz, H. Render

The existence of decompositions of the form $f = P \cdot q + r$ with $P_{k}^{*} (D) r = 0$ , where $f$ is entire, $P$ a polynomial and $P_{k}^{*}$ the principal part of $P$ wi…

math.AP2024

Asympotic bounds for Bombieri's inequality on products of homogeneous polynomials

J. M. Aldaz, H. Render

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 hom…