@unpublished{52691, abstract = {{We prove Feynman-Kac formulas for the semigroups generated by selfadjoint operators in a class containing Fr\"ohlich Hamiltonians known from solid state physics. The latter model multi-polarons, i.e., a fixed number of quantum mechanical electrons moving in a polarizable crystal and interacting with the quantized phonon field generated by the crystal's vibrational modes. Both the electrons and phonons can be confined to suitable open subsets of Euclidean space. We also include possibly very singular magnetic vector potentials and electrostatic potentials. Our Feynman-Kac formulas comprise Fock space operator-valued multiplicative functionals and can be applied to every vector in the underlying Hilbert space. In comparison to the renormalized Nelson model, for which analogous Feynman-Kac formulas are known, the analysis of the creation and annihilation terms in the multiplicative functionals requires novel ideas to overcome difficulties caused by the phonon dispersion relation being constant. Getting these terms under control and generalizing other construction steps so as to cover confined systems are the main achievements of this article.}}, author = {{Hinrichs, Benjamin and Matte, Oliver}}, booktitle = {{arXiv:2403.12147}}, title = {{{Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains}}}, year = {{2024}}, } @article{53542, abstract = {{AbstractThis work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G/K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$ L 1 initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-K-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-K-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G/K. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$ L 1 asymptotic convergence without the assumption of bi-K-invariance.}}, author = {{Papageorgiou, Efthymia}}, issn = {{1424-3199}}, journal = {{Journal of Evolution Equations}}, keywords = {{Mathematics (miscellaneous)}}, number = {{2}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}}}, doi = {{10.1007/s00028-024-00959-6}}, volume = {{24}}, year = {{2024}}, } @article{51207, abstract = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the asymptotic growth of $\Gamma$ in the two direction defined by the two factors. We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of $\Gamma$.}}, author = {{Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Geom Dedicata}}, title = {{{Temperedness of locally symmetric spaces: The product case}}}, doi = {{https://doi.org/10.1007/s10711-024-00904-4}}, volume = {{218}}, year = {{2024}}, } @book{55193, author = {{Hoffmann, Max and Hilgert, Joachim and Weich, Tobias}}, isbn = {{9783662673560}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik}}}, doi = {{10.1007/978-3-662-67357-7}}, year = {{2024}}, } @article{53300, author = {{Brennecken, Dominik}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{2}}, publisher = {{Elsevier BV}}, title = {{{Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}}}, doi = {{10.1016/j.jmaa.2024.128125}}, volume = {{535}}, year = {{2024}}, } @inbook{56001, author = {{Brennecken, Dominik and Rösler, Margit}}, booktitle = {{Women in Analysis and PDE}}, editor = {{Chatzakou, Marianna and Ruzhansky, Michael and Stoeva, Diana}}, isbn = {{978-3-031-57004-9}}, pages = {{425}}, publisher = {{Birkhäuser Cham}}, title = {{{The Laplace transform in Dunkl theory}}}, volume = {{5}}, year = {{2024}}, } @unpublished{56114, author = {{Pinaud, Matthieu}}, title = {{{Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups}}}, year = {{2024}}, } @unpublished{56116, author = {{Glöckner, Helge and Grong, Erlend and Schmeding, Alexander}}, title = {{{Boundary values of diffeomorphisms of simple polytopes, and controllability}}}, year = {{2024}}, } @article{56366, abstract = {{AbstractWe discuss in which cases the Dunkl convolution of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system we consider the Riesz distributions and prove that their Dunkl convolution exists and that  holds.}}, author = {{Brennecken, Dominik}}, issn = {{0025-584X}}, journal = {{Mathematische Nachrichten}}, publisher = {{Wiley}}, title = {{{Dunkl convolution and elliptic regularity for Dunkl operators}}}, doi = {{10.1002/mana.202300370}}, year = {{2024}}, } @article{56584, author = {{Suri, Ali}}, journal = {{Journal of Geometry and Physics}}, pages = {{105109}}, title = {{{Curvature and stability of quasi-geostrophic motion}}}, volume = {{198}}, year = {{2024}}, } @article{56585, author = {{Suri, Ali}}, journal = {{Journal of Geometry and Physics}}, pages = {{105333}}, title = {{{Conjugate points along spherical harmonics}}}, volume = {{206}}, year = {{2024}}, } @unpublished{56583, author = {{Glöckner, Helge and Suri, Ali}}, title = {{{L^1-regularity of strong ILB-Lie groups}}}, year = {{2024}}, } @inproceedings{63605, author = {{Tomasz Goliński, Tomasz and Rahangdale, Praful and Tumpach, Alice Barbora}}, booktitle = {{Geometric Methods in Physics, XLI Workshop}}, editor = {{Kielanowski, P. and Dobrogowska, A. and Fernández, D. and Goliński, D.}}, isbn = {{978-3-031-89857-0}}, location = {{Białystok, Poland}}, pages = {{97–117}}, publisher = {{Birkhauser}}, title = {{{Poisson structures in the Banach setting: comparison of different approaches}}}, doi = {{10.1007/978-3-031-89857-0_9}}, year = {{2024}}, } @article{63636, author = {{Hinrichs, Benjamin and Lampart, Jonas}}, issn = {{1631-073X}}, journal = {{Comptes Rendus. Mathématique}}, number = {{G11}}, pages = {{1399--1411}}, publisher = {{MathDoc/Centre Mersenne}}, title = {{{A Lower Bound on the Critical Momentum of an Impurity in a Bose–Einstein Condensate}}}, doi = {{10.5802/crmath.652}}, volume = {{362}}, year = {{2024}}, } @unpublished{63641, abstract = {{We present a simple functional integration based proof that the semigroups generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians are positivity improving (and hence ergodic) with respect to the Fröhlich cone for arbitrary values of the total momentum. Our argument simplifies known proofs for ergodicity and the result is new in the semi-relativistic case.}}, author = {{Hinrichs, Benjamin and Hiroshima, Fumio}}, booktitle = {{arXiv:2412.09708}}, title = {{{On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups}}}, year = {{2024}}, } @article{63637, author = {{Hinrichs, Benjamin and Lemm, Marius and Siebert, Oliver}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, number = {{1}}, pages = {{41--80}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{On Lieb–Robinson Bounds for a Class of Continuum Fermions}}}, doi = {{10.1007/s00023-024-01453-y}}, volume = {{26}}, year = {{2024}}, } @article{51374, author = {{Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}}, issn = {{0022-1236}}, journal = {{Journal of Functional Analysis}}, keywords = {{Analysis}}, number = {{7}}, publisher = {{Elsevier BV}}, title = {{{Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively}}}, doi = {{10.1016/j.jfa.2024.110319}}, volume = {{286}}, year = {{2024}}, } @article{32101, author = {{Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}}, journal = {{J. Europ. Math. Soc.}}, number = {{8}}, pages = {{3085–3147}}, title = {{{Ruelle-Taylor resonances of Anosov actions}}}, doi = {{https://doi.org/10.4171/JEMS/1428}}, volume = {{27}}, year = {{2024}}, } @unpublished{57582, abstract = {{We prove that the Patterson-Sullivan and Wigner distributions on the unit sphere bundle of a convex-cocompact hyperbolic surface are asymptotically identical. This generalizes results in the compact case by Anantharaman-Zelditch and Hansen-Hilgert-Schr\"oder.}}, author = {{Delarue, Benjamin and Palmirotta, Guendalina}}, booktitle = {{arXiv:2411.19782}}, title = {{{Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces}}}, year = {{2024}}, } @article{32097, author = {{Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}}, journal = {{Journal of Differential Geometry}}, pages = {{959--1026}}, title = {{{SRB Measures of Anosov Actions}}}, doi = {{ DOI: 10.4310/jdg/1729092452}}, volume = {{128}}, year = {{2024}}, }