H. Render

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math.AP2026

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.AP2026

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…