{"oa":"1","citation":{"ieee":"L. Langen and M. Rösler, “Multiresolution analysis on spectra of hermitian matrices,” <i>arXiv:2410.10364</i>. 2024.","bibtex":"@article{Langen_Rösler_2024, title={Multiresolution analysis on spectra of hermitian matrices}, journal={arXiv:2410.10364}, author={Langen, Lukas and Rösler, Margit}, year={2024} }","apa":"Langen, L., &#38; Rösler, M. (2024). Multiresolution analysis on spectra of hermitian matrices. In <i>arXiv:2410.10364</i>.","mla":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>ArXiv:2410.10364</i>, 2024.","short":"L. Langen, M. Rösler, ArXiv:2410.10364 (2024).","chicago":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>ArXiv:2410.10364</i>, 2024.","ama":"Langen L, Rösler M. Multiresolution analysis on spectra of hermitian matrices. <i>arXiv:241010364</i>. Published online 2024."},"related_material":{"link":[{"relation":"confirmation","url":"https://arxiv.org/abs/2410.10364"}]},"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"}],"ddc":["510"],"title":"Multiresolution analysis on spectra of hermitian matrices","publication":"arXiv:2410.10364","project":[{"grant_number":"491392403","name":"TRR 358 - Ganzzahlige Strukturen in Geometrie und Darstellungstheorie","_id":"357"}],"_id":"56717","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2410.10364"}],"year":"2024","author":[{"first_name":"Lukas","full_name":"Langen, Lukas","last_name":"Langen","id":"73664"},{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"}],"file":[{"content_type":"application/pdf","file_name":"MSA_hermitsch_arxivSub.pdf","file_id":"56720","date_created":"2024-10-22T09:47:14Z","success":1,"access_level":"closed","file_size":438938,"relation":"main_file","creator":"llangen","date_updated":"2024-10-22T09:47:14Z"}],"status":"public","date_created":"2024-10-22T09:31:19Z","has_accepted_license":"1","user_id":"73664","external_id":{"arxiv":["2410.10364"]},"department":[{"_id":"555"}],"date_updated":"2024-10-22T09:53:41Z","file_date_updated":"2024-10-22T09:47:14Z","type":"preprint"}