@misc{51565,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{263–264}},
title = {{{Jost-Hinrich Eschenburg: Sternstunden der Mathematik. Springer 2017}}},
doi = {{10.1007/s00591-019-00247-2}},
volume = {{66}},
year = {{2019}},
}
@article{53416,
abstract = {{Abstract
For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.}},
author = {{Küster, Benjamin and Weich, Tobias}},
issn = {{1073-7928}},
journal = {{International Mathematics Research Notices}},
keywords = {{General Mathematics}},
number = {{11}},
pages = {{8225--8296}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}}},
doi = {{10.1093/imrn/rnz068}},
volume = {{2021}},
year = {{2019}},
}
@unpublished{64769,
author = {{Nikitin, Natalie}},
title = {{{Measurable regularity of infinite-dimensional Lie groups based on Lusin measurability}}},
year = {{2019}},
}
@article{64756,
author = {{Walter, Boris}},
issn = {{0019-3577}},
journal = {{Indagationes Mathematicae}},
keywords = {{58D05, 57S05, 22E65, 58D15, 58B10}},
number = {{4}},
pages = {{669–705}},
title = {{{Weighted diffeomorphism groups of Riemannian manifolds}}},
doi = {{10.1016/j.indag.2019.03.003}},
volume = {{30}},
year = {{2019}},
}
@article{64630,
author = {{Glöckner, Helge}},
issn = {{0008-414X}},
journal = {{Canadian Journal of Mathematics}},
keywords = {{22E65, 22A05, 22E67, 46A13, 46M40, 58D05}},
number = {{1}},
pages = {{131–152}},
title = {{{Completeness of infinite-dimensional Lie groups in their left uniformity}}},
doi = {{10.4153/CJM-2017-048-5}},
volume = {{71}},
year = {{2019}},
}
@article{34664,
author = {{Black, Tobias}},
issn = {{0036-1410}},
journal = {{SIAM Journal on Mathematical Analysis}},
keywords = {{Applied Mathematics, Computational Mathematics, Analysis}},
number = {{4}},
pages = {{4087--4116}},
publisher = {{Society for Industrial & Applied Mathematics (SIAM)}},
title = {{{Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion}}},
doi = {{10.1137/17m1159488}},
volume = {{50}},
year = {{2018}},
}
@article{34666,
author = {{Black, Tobias}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
keywords = {{Analysis, Applied Mathematics}},
number = {{5}},
pages = {{2296--2339}},
publisher = {{Elsevier BV}},
title = {{{Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D}}},
doi = {{10.1016/j.jde.2018.04.035}},
volume = {{265}},
year = {{2018}},
}
@article{34667,
author = {{Black, Tobias}},
issn = {{0362-546X}},
journal = {{Nonlinear Analysis}},
keywords = {{Applied Mathematics, Analysis}},
pages = {{129--153}},
publisher = {{Elsevier BV}},
title = {{{Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions}}},
doi = {{10.1016/j.na.2018.10.003}},
volume = {{180}},
year = {{2018}},
}
@article{51388,
author = {{Hilgert, Joachim and Wurzbacher, T. and Alldridge, A.}},
journal = {{Journal of the Institute of Mathematics of Jussieu}},
pages = {{1065--1120}},
title = {{{Superorbits}}},
doi = {{10.1017/S147474801600030X}},
volume = {{17}},
year = {{2018}},
}
@inbook{51462,
author = {{Hilgert, Joachim}},
booktitle = {{Erscheinung und Vernunft - Wirklichkeitszugänge der Aufklärung}},
editor = {{Nieland, T.}},
publisher = {{Frank&Timme}},
title = {{{Von Fermat und Descartes zu Gauß und Cauchy - Der Wandel der Mathematik in der Zeit der Aufklärung}}},
year = {{2018}},
}
@unpublished{51523,
author = {{Hilgert, Joachim and Hansen, S. and Parthasarathy, A.}},
title = {{{Boundary Values of Eigenfunctions on Riemannian Symmetric Spaces}}},
year = {{2018}},
}
@misc{51571,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{307--309}},
title = {{{Winfried Scharlau: Das Glück, Mathematiker zu sein – Friedrich Hirzebruch und seine Zeit (Springer Spektrum 2017)}}},
volume = {{65}},
year = {{2018}},
}
@misc{51572,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{129--131}},
title = {{{Lemmermeyer, F: Quadratische Zahlkörper – Eine Einführung mit vielen Beispielen (Springer Spektrum 2017)}}},
volume = {{65}},
year = {{2018}},
}
@misc{51570,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{311--313}},
title = {{{Barry Mazur und William Stein: Prime Numbers and the Riemann Hypothesis}}},
volume = {{65}},
year = {{2018}},
}
@misc{51574,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{121--123}},
title = {{{Joseph, G.G. Indian Mathematics. Engaging with the World from Ancient to Modern Times (World Scientific 2016)}}},
volume = {{65}},
year = {{2018}},
}
@misc{51573,
author = {{Hilgert, Joachim}},
booktitle = {{Mathematische Semesterberichte}},
pages = {{125--127}},
title = {{{Diaconis, P., B. Skyrms: Ten great ideas about chance (Princeton University Press 2018)}}},
volume = {{65}},
year = {{2018}},
}
@article{37661,
author = {{Rösler, Margit and Voit, Michael}},
issn = {{0022-2526}},
journal = {{Studies in Applied Mathematics}},
keywords = {{Applied Mathematics}},
number = {{4}},
pages = {{474--500}},
publisher = {{Wiley}},
title = {{{Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones}}},
doi = {{10.1111/sapm.12217}},
volume = {{141}},
year = {{2018}},
}
@article{37662,
author = {{Rösler, Margit and Graczyk, Piotr and Luks, Tomasz}},
issn = {{0926-2601}},
journal = {{Potential Analysis}},
keywords = {{Analysis}},
number = {{3}},
pages = {{337--360}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{On the Green Function and Poisson Integrals of the Dunkl Laplacian}}},
doi = {{10.1007/s11118-017-9638-6}},
volume = {{48}},
year = {{2018}},
}
@article{40050,
author = {{Baeumer, Boris and Luks, Tomasz and Meerschaert, Mark M.}},
issn = {{0025-584X}},
journal = {{Mathematische Nachrichten}},
keywords = {{General Mathematics}},
number = {{17-18}},
pages = {{2516--2535}},
publisher = {{Wiley}},
title = {{{Space‐time fractional Dirichlet problems}}},
doi = {{10.1002/mana.201700111}},
volume = {{291}},
year = {{2018}},
}
@inbook{64633,
author = {{Glöckner, Helge}},
booktitle = {{New directions in locally compact groups}},
isbn = {{978-1-108-41312-1; 978-1-108-33267-5}},
keywords = {{22E50, 22E20, 22D05, 22E35, 26E30, 37D10}},
pages = {{37–72}},
publisher = {{Cambridge: Cambridge University Press}},
title = {{{Lectures on Lie groups over local fields}}},
doi = {{10.1017/9781108332675.005}},
year = {{2018}},
}