Hermann Render

will speak on

Uniqueness results for entire harmonic functions and for Fischer decompositions

Time: 3:00PM
Date: Tue 5th March 2024
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: In this talk we shall present sufficient conditions such that an entire harmonic function of sufficiently low order which vanishes on the zero-set of a given irreducible polynomial $P(x)$ of degree $2k$ is identically zero. It is assumed that the leading homogeneous part $P_2k$ of $P(x)$ is non-negative and satisfies for each natural number $m$ a lower integral estimate for all homogeneous polynomial of degree $m$. In particular it is shown that an entire harmonic function of order smaller than $1/2$ which vanishes on the boundary of a paraboloid is identically zero. Further applications are uniqueness results for Fischer decompositions.

This is joint work with J.M. Aldaz (Universidad Autonoma de Madrid).

https://ucd-ie.zoom.us/j/69673850551

(This talk is part of the Analysis series.)

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