@article{KrausMouchaRoth2022,
  author    = {Kraus, Daniela and Moucha, Annika and Roth, Oliver},
  title     = {A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights},
  series = {Analysis and Mathematical Physics},
  volume    = {12},
  journal   = {Analysis and Mathematical Physics},
  number    = {1},
  issn      = {1664-235X},
  doi       = {10.1007/s13324-021-00639-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-270485},
  year      = {2022},
  abstract  = {We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil (Int. Math. Res. Not. 2019: 3301-3312, 2019) on the weighted martingale Carleson embedding theorem with matrix weights. In the scalar case this new upper bound is optimal.},
  language  = {en}
}
@article{HeinsRothWaldmann2023,
  author    = {Heins, Michael and Roth, Oliver and Waldmann, Stefan},
  title     = {Convergent star products on cotangent bundles of Lie groups},
  series = {Mathematische Annalen},
  volume    = {386},
  journal   = {Mathematische Annalen},
  number    = {1-2},
  issn      = {0025-5831},
  doi       = {10.1007/s00208-022-02384-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324324},
  pages     = {151-206},
  year      = {2023},
  abstract  = {For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T\(^*\)G thanks to its homogeneity. We define a nuclear Fr{\´e}chet algebra of certain analytic functions on T\(^*\)G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter \(\hbar\). This nuclear Fr{\´e}chet algebra is realized as the completed (projective) tensor product of a nuclear Fr{\´e}chet algebra of entire functions on G with an appropriate nuclear Fr{\´e}chet algebra of functions on \({\mathfrak {g}}^*\). The passage to the Weyl-ordered star product, i.e. the Gutt star product on T\(^*\)G, is shown to preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on \(\hbar\).},
  language  = {en}
}