H. Render

most citedA Fischer type decomposition theorem from the apolar inner product

3 citations · 3 across the 2 of their papers we have counts for

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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.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…