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A complex Lie algebra of rotationally symmetric operators and their harmonics

Klintborg, Markus LU (2026) In Journal of Analysis
Abstract

We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which such generalised harmonic functions derive. We show that every one of these solutions have a canonical series representation and retrieve those obtained in the case of Laplace and Helmholtz equation. These sums are given in confluent hypergeometric terms that asymptotically correspond to the complex exponential function.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Bessel function, Confluent hypergeometric function, Harmonic function, Power series
in
Journal of Analysis
publisher
Springer Science and Business Media B.V.
external identifiers
  • scopus:105036196351
ISSN
0971-3611
DOI
10.1007/s41478-026-01073-1
language
English
LU publication?
yes
id
4122088d-e3f2-4277-85e0-25c49483c93f
date added to LUP
2026-05-20 15:16:09
date last changed
2026-05-20 15:17:09
@article{4122088d-e3f2-4277-85e0-25c49483c93f,
  abstract     = {{<p>We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which such generalised harmonic functions derive. We show that every one of these solutions have a canonical series representation and retrieve those obtained in the case of Laplace and Helmholtz equation. These sums are given in confluent hypergeometric terms that asymptotically correspond to the complex exponential function.</p>}},
  author       = {{Klintborg, Markus}},
  issn         = {{0971-3611}},
  keywords     = {{Bessel function; Confluent hypergeometric function; Harmonic function; Power series}},
  language     = {{eng}},
  publisher    = {{Springer Science and Business Media B.V.}},
  series       = {{Journal of Analysis}},
  title        = {{A complex Lie algebra of rotationally symmetric operators and their harmonics}},
  url          = {{http://dx.doi.org/10.1007/s41478-026-01073-1}},
  doi          = {{10.1007/s41478-026-01073-1}},
  year         = {{2026}},
}