@article{34832, author = {{Hanusch, Maximilian}}, journal = {{Annals of Global Analysis and Geometry}}, keywords = {{Lax equation, generalized Baker-Campbell-Dynkin-Hausdorff formula, regularity of Lie groups}}, number = {{21}}, title = {{{The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}}}, doi = {{10.1007/s10455-023-09888-y}}, volume = {{63}}, year = {{2023}}, } @article{34833, author = {{Hanusch, Maximilian}}, journal = {{Indagationes Mathematicae.}}, keywords = {{Lie group actions and analytic 1-submanifolds}}, number = {{4}}, pages = {{752--811}}, title = {{{Decompositions of Analytic 1-Manifolds}}}, doi = {{10.1016/j.indag.2023.02.003}}, volume = {{34}}, year = {{2023}}, } @article{63635, author = {{Hinrichs, Benjamin and Matte, Oliver}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, number = {{6}}, pages = {{2877--2940}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions}}}, doi = {{10.1007/s00023-023-01369-z}}, volume = {{25}}, year = {{2023}}, } @article{46100, author = {{Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{1}}, publisher = {{Elsevier BV}}, title = {{{Super-Gaussian decay of exponentials: A sufficient condition}}}, doi = {{10.1016/j.jmaa.2023.127558}}, volume = {{528}}, year = {{2023}}, } @article{31190, abstract = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle-Taylor resonances and establish a spectral gap which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e. a 1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on $G/K$.}}, author = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Analysis & PDE}}, number = {{10}}, pages = {{2241–2265}}, publisher = {{MSP}}, title = {{{Higher rank quantum-classical correspondence}}}, doi = {{https://doi.org/10.2140/apde.2023.16.2241}}, volume = {{16}}, year = {{2023}}, } @article{31059, abstract = {{In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.}}, author = {{Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}}, journal = {{Communications in Mathematical Physics}}, pages = {{655--678}}, title = {{{Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}}}, doi = {{https://doi.org/10.1007/s00220-022-04538-z}}, volume = {{398}}, year = {{2023}}, } @article{51383, author = {{Hilgert, Joachim and Arends, C.}}, journal = {{J. de l'École polytechnique — Mathématiques}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}}}, volume = {{10}}, year = {{2023}}, } @article{51384, author = {{Hilgert, Joachim and Glöckner, H.}}, journal = {{J. Diff. Equations}}, pages = {{186--232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, volume = {{343}}, year = {{2023}}, } @article{53540, abstract = {{AbstractThis note is concerned with two families of operators related to the fractional Laplacian, the first arising from the Caffarelli-Silvestre extension problem and the second from the fractional heat equation. They both include the Poisson semigroup. We show that on a complete, connected, and non-compact Riemannian manifold of non-negative Ricci curvature, in both cases, the solution with $$L^1$$ L 1 initial data behaves asymptotically as the mass times the fundamental solution. Similar long-time convergence results remain valid on more general manifolds satisfying the Li-Yau two-sided estimate of the heat kernel. The situation changes drastically on hyperbolic space, and more generally on rank one non-compact symmetric spaces: we show that for the Poisson semigroup, the convergence to the Poisson kernel fails -but remains true under the additional assumption of radial initial data.}}, author = {{Papageorgiou, Efthymia}}, issn = {{0926-2601}}, journal = {{Potential Analysis}}, keywords = {{Analysis}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds}}}, doi = {{10.1007/s11118-023-10109-1}}, year = {{2023}}, } @article{53539, abstract = {{AbstractThe infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length T around a fixed origin when $$T \rightarrow +\infty $$ T → + ∞ . The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces G/K of noncompact type and of general rank. This amounts to the behavior of solutions to the heat equation subject to the Doob transform induced by the ground spherical function. Unlike the standard Brownian motion, we observe in this case phenomena which are similar to the Euclidean setting, namely $$L^1$$ L 1 asymptotic convergence without requiring bi-K-invariance for initial data, and strong $$L^{\infty }$$ L ∞ convergence.}}, author = {{Papageorgiou, Efthymia}}, issn = {{2296-9020}}, journal = {{Journal of Elliptic and Parabolic Equations}}, keywords = {{Applied Mathematics, Numerical Analysis, Analysis}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Asymptotics for the infinite Brownian loop on noncompact symmetric spaces}}}, doi = {{10.1007/s41808-023-00250-8}}, year = {{2023}}, } @article{31982, abstract = {{AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $$\Sigma $$ Σ with Betti number $$b_1$$ b 1 , the order of vanishing of the Ruelle zeta function at zero equals $$4-b_1$$ 4 - b 1 , while in the hyperbolic case it is equal to $$4-2b_1$$ 4 - 2 b 1 . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle $$S\Sigma $$ S Σ with harmonic 1-forms on $$\Sigma $$ Σ .}}, author = {{Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}}, issn = {{0020-9910}}, journal = {{Inventiones mathematicae}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{303--394}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}}}, doi = {{10.1007/s00222-022-01108-x}}, volume = {{229}}, year = {{2022}}, } @article{34792, author = {{Glöckner, Helge}}, issn = {{2070-0466}}, journal = {{p-Adic Numbers, Ultrametric Analysis, and Applications}}, keywords = {{20Exx, 22Exx, 32Cxx}}, number = {{2}}, pages = {{138–144}}, title = {{{Non-Lie subgroups in Lie groups over local fields of positive characteristic}}}, doi = {{10.1134/S2070046622020042}}, volume = {{14}}, year = {{2022}}, } @article{34791, author = {{Glöckner, Helge and Schmeding, Alexander}}, issn = {{0232-704X}}, journal = {{Annals of Global Analysis and Geometry}}, keywords = {{58D15, 22E65, 26E15, 26E20, 46E40, 46T20, 58A05}}, number = {{2}}, pages = {{359–398}}, title = {{{Manifolds of mappings on Cartesian products}}}, doi = {{10.1007/s10455-021-09816-y}}, volume = {{61}}, year = {{2022}}, } @article{34796, abstract = {{We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E×E is a kR-space.}}, author = {{Glöckner, Helge}}, issn = {{2075-1680}}, journal = {{Axioms}}, number = {{5}}, title = {{{Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}}}, doi = {{10.3390/axioms11050221}}, volume = {{11}}, year = {{2022}}, } @unpublished{34804, abstract = {{Starting with a finite-dimensional complex Lie algebra, we extend scalars using suitable commutative topological algebras. We study Birkhoff decompositions for the corresponding loop groups. Some results remain valid for loop groups with valued in complex Banach-Lie groups.}}, author = {{Glöckner, Helge}}, booktitle = {{arXiv:2206.11711}}, title = {{{Birkhoff decompositions for loop groups with coefficient algebras}}}, year = {{2022}}, } @article{35306, author = {{Guedes Bonthonneau, Yannick and Weich, Tobias}}, issn = {{1435-9855}}, journal = {{Journal of the European Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{3}}, pages = {{851--923}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}}}, doi = {{10.4171/jems/1103}}, volume = {{24}}, year = {{2022}}, } @article{34817, author = {{Hanusch, Maximilian}}, issn = {{1019-8385}}, journal = {{Communications in Analysis and Geometry}}, keywords = {{regularity of Lie groups}}, number = {{1}}, pages = {{53--152}}, publisher = {{International Press of Boston}}, title = {{{Regularity of Lie groups}}}, doi = {{10.4310/cag.2022.v30.n1.a2}}, volume = {{30}}, year = {{2022}}, } @techreport{34856, author = {{Hanusch, Maximilian}}, pages = {{385}}, publisher = {{https://maximilianhanusch.wixsite.com/my-site/lehre-teaching}}, title = {{{Analysis 1 und 2 Skript/Buch}}}, year = {{2022}}, } @article{31057, abstract = {{In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.}}, author = {{Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}}, journal = {{Journal of Physics A: Mathematical and Theoretical}}, number = {{24}}, publisher = {{IOP Publishing Ltd}}, title = {{{Semiclassical formulae For Wigner distributions}}}, doi = {{10.1088/1751-8121/ac6d2b}}, volume = {{55}}, year = {{2022}}, } @article{35322, author = {{Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}}, issn = {{1664-039X}}, journal = {{Journal of Spectral Theory}}, keywords = {{Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{659--681}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Poisson transforms for trees of bounded degree}}}, doi = {{10.4171/jst/414}}, volume = {{12}}, year = {{2022}}, }