SPACES OF k-MODIFIED HARMONIC POLYNOMIALS
Katholische Universit¨at Eichst¨att-Ingolstadt, Mathematisch-Geographische Fakult¨at, 85071 Eichst¨att, Germany [email protected], ELEUTHERIUS SYMEONIDIS · Revue Roumaine Mathematiques Pures Appliquees · 2024
The polynomials u on Rd (d ≥ 2) that satisfy the equation xd ·Δu+k · ∂u ∂xd = 0 (k ∈ R) are called k-modified harmonic. In this article, we study the dimension of the space of homogeneous such polynomials of a fixed degree.