[{"external_id":{"arxiv":["2410.10364"]},"language":[{"iso":"eng"}],"ddc":["510"],"publication":"Indagationes Mathematicae","file":[{"relation":"main_file","success":1,"content_type":"application/pdf","file_name":"MSA_hermitsch_published.pdf","access_level":"closed","file_id":"64288","file_size":443262,"date_created":"2026-02-19T14:14:39Z","creator":"llangen","date_updated":"2026-02-19T14:14:39Z"}],"abstract":[{"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.","lang":"eng"}],"date_created":"2024-10-22T09:31:19Z","publisher":"Elsevier","title":"Multiresolution analysis on spectra of hermitian matrices","issue":"6","year":"2025","user_id":"73664","department":[{"_id":"555"}],"project":[{"_id":"357","name":"TRR 358 - Ganzzahlige Strukturen in Geometrie und Darstellungstheorie"}],"_id":"56717","file_date_updated":"2026-02-19T14:14:39Z","article_type":"original","type":"journal_article","status":"public","author":[{"first_name":"Lukas","full_name":"Langen, Lukas","id":"73664","last_name":"Langen"},{"last_name":"Rösler","full_name":"Rösler, Margit","id":"37390","first_name":"Margit"}],"volume":36,"date_updated":"2026-02-19T14:16:43Z","main_file_link":[{"url":"https://doi.org/10.1016/j.indag.2025.03.009"}],"related_material":{"link":[{"relation":"research_paper","url":"https://arxiv.org/abs/2410.10364"}]},"publication_status":"published","has_accepted_license":"1","citation":{"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.","chicago":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>Indagationes Mathematicae</i> 36, no. 6 (2025): 1671–94.","ama":"Langen L, Rösler M. Multiresolution analysis on spectra of hermitian matrices. <i>Indagationes Mathematicae</i>. 2025;36(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} }","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.","apa":"Langen, L., &#38; Rösler, M. (2025). Multiresolution analysis on spectra of hermitian matrices. <i>Indagationes Mathematicae</i>, <i>36</i>(6), 1671–1694."},"intvolume":"        36","page":"1671-1694"}]