@article{56717,
  abstract     = {{We establish a multiresolution analysis on the space $\text{Herm}(n)$ of
$n\times n$ complex Hermitian matrices which is adapted to invariance under
conjugation by the unitary group $U(n).$ The orbits under this action are
parametrized by the possible ordered spectra of Hermitian matrices, which
constitute a closed Weyl chamber of type $A_{n-1}$ in $\mathbb R^n.$ The space
$L^2(\text{Herm}(n))^{U(n)}$ of radial, i.e. $U(n)$-invariant $L^2$-functions
on $\text{Herm}(n)$ is naturally identified with a certain weighted $L^2$-space
on this chamber.
  The scale spaces of our multiresolution analysis are obtained by usual dyadic
dilations as well as generalized translations of a scaling function, where the
generalized translation is a hypergroup translation which respects the radial
geometry. We provide a concise criterion to characterize orthonormal wavelet
bases and show that such bases always exist. They provide natural orthonormal
bases of the space $L^2(\text{Herm}(n))^{U(n)}.$
  Furthermore, we show how to obtain radial scaling functions from classical
scaling functions on $\mathbb R^{n}$. Finally, generalizations related to the
Cartan decompositions for general compact Lie groups are indicated.}},
  author       = {{Langen, Lukas and Rösler, Margit}},
  journal      = {{Indagationes Mathematicae}},
  number       = {{6}},
  pages        = {{1671--1694}},
  publisher    = {{Elsevier}},
  title        = {{{Multiresolution analysis on spectra of hermitian matrices}}},
  volume       = {{36}},
  year         = {{2025}},
}