TL;DR
This paper introduces a framework for modeling generalized harmonic functions using differential operators and complex spaces, exploring their properties, relations, and cellular decomposition, advancing the theoretical understanding of harmonic analysis.
Contribution
It develops a novel approach to generalized harmonic functions within the Weyl-algebra context, linking them to polyharmonic functions and their cellular structure.
Findings
Characterization of differential operators commuting with rotations
Relationship between generalized harmonic functions and polyharmonic functions
Retrieval of cellular decomposition for polyharmonic functions
Abstract
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such functions. We also investigate how such functions are related, and retrieve the cellular decomposition for polyharmonic functions.
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