---
_id: '56717'
abstract:
- lang: eng
  text: "We establish a multiresolution analysis on the space $\\text{Herm}(n)$ of\r\n$n\\times
    n$ complex Hermitian matrices which is adapted to invariance under\r\nconjugation
    by the unitary group $U(n).$ The orbits under this action are\r\nparametrized
    by the possible ordered spectra of Hermitian matrices, which\r\nconstitute a closed
    Weyl chamber of type $A_{n-1}$ in $\\mathbb R^n.$ The space\r\n$L^2(\\text{Herm}(n))^{U(n)}$
    of radial, i.e. $U(n)$-invariant $L^2$-functions\r\non $\\text{Herm}(n)$ is naturally
    identified with a certain weighted $L^2$-space\r\non this chamber.\r\n  The scale
    spaces of our multiresolution analysis are obtained by usual dyadic\r\ndilations
    as well as generalized translations of a scaling function, where the\r\ngeneralized
    translation is a hypergroup translation which respects the radial\r\ngeometry.
    We provide a concise criterion to characterize orthonormal wavelet\r\nbases and
    show that such bases always exist. They provide natural orthonormal\r\nbases of
    the space $L^2(\\text{Herm}(n))^{U(n)}.$\r\n  Furthermore, we show how to obtain
    radial scaling functions from classical\r\nscaling functions on $\\mathbb R^{n}$.
    Finally, generalizations related to the\r\nCartan decompositions for general compact
    Lie groups are indicated."
article_type: original
author:
- first_name: Lukas
  full_name: Langen, Lukas
  id: '73664'
  last_name: Langen
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Langen L, Rösler M. Multiresolution analysis on spectra of hermitian matrices.
    <i>Indagationes Mathematicae</i>. 2025;36(6):1671-1694.
  apa: Langen, L., &#38; Rösler, M. (2025). Multiresolution analysis on spectra of
    hermitian matrices. <i>Indagationes Mathematicae</i>, <i>36</i>(6), 1671–1694.
  bibtex: '@article{Langen_Rösler_2025, title={Multiresolution analysis on spectra
    of hermitian matrices}, volume={36}, number={6}, journal={Indagationes Mathematicae},
    publisher={Elsevier}, author={Langen, Lukas and Rösler, Margit}, year={2025},
    pages={1671–1694} }'
  chicago: 'Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra
    of Hermitian Matrices.” <i>Indagationes Mathematicae</i> 36, no. 6 (2025): 1671–94.'
  ieee: L. Langen and M. Rösler, “Multiresolution analysis on spectra of hermitian
    matrices,” <i>Indagationes Mathematicae</i>, vol. 36, no. 6, pp. 1671–1694, 2025.
  mla: Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian
    Matrices.” <i>Indagationes Mathematicae</i>, vol. 36, no. 6, Elsevier, 2025, pp.
    1671–94.
  short: L. Langen, M. Rösler, Indagationes Mathematicae 36 (2025) 1671–1694.
date_created: 2024-10-22T09:31:19Z
date_updated: 2026-02-19T14:16:43Z
ddc:
- '510'
department:
- _id: '555'
external_id:
  arxiv:
  - '2410.10364'
file:
- access_level: closed
  content_type: application/pdf
  creator: llangen
  date_created: 2026-02-19T14:14:39Z
  date_updated: 2026-02-19T14:14:39Z
  file_id: '64288'
  file_name: MSA_hermitsch_published.pdf
  file_size: 443262
  relation: main_file
  success: 1
file_date_updated: 2026-02-19T14:14:39Z
has_accepted_license: '1'
intvolume: '        36'
issue: '6'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1016/j.indag.2025.03.009
page: 1671-1694
project:
- _id: '357'
  name: TRR 358 - Ganzzahlige Strukturen in Geometrie und Darstellungstheorie
publication: Indagationes Mathematicae
publication_status: published
publisher: Elsevier
related_material:
  link:
  - relation: research_paper
    url: https://arxiv.org/abs/2410.10364
status: public
title: Multiresolution analysis on spectra of hermitian matrices
type: journal_article
user_id: '73664'
volume: 36
year: '2025'
...