@article{35574, author = {{Winkler, Michael}}, journal = {{Proceedings of the London Mathematical Society}}, pages = {{133--181}}, title = {{{A family of mass-critical Keller-Segel systems.}}}, volume = {{124}}, year = {{2022}}, } @article{35483, author = {{ Kang, Kyungkeun and Lee, Jihoon and Winkler, Michael}}, journal = {{Discrete and Continuous Dynamical Systems}}, pages = {{5201--5222}}, title = {{{Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$.}}}, volume = {{42}}, year = {{2022}}, } @article{38039, abstract = {{We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$ and a varying constant $κ\in\,[0,\infty[$. Using elementary symmetric functions, we present polynomials which are simultaneous eigenfunctions of the $L_k$ for all $κ\in\,]0,\infty[$. This leads to martingales associated with the Heckman-Opdam diffusions $ (X_{t,1},\ldots,X_{t,N})_{t\ge0}$. As our results extend to the freezing case $κ=\infty$ with a deterministic limit after some renormalization, we find formulas for the expectations $\mathbb E(\prod_{j=1}^N(y-X_{t,j})),$ $y\in\mathbb C$.}}, author = {{Rösler, Margit and Voit, Michael}}, journal = {{Contemporary Mathematics}}, number = {{780}}, pages = {{243--262}}, title = {{{Elementary symmetric polynomials and martingales for Heckman-Opdam processes}}}, doi = {{10.48550/ARXIV.2108.03228}}, year = {{2022}}, } @article{35479, author = {{Bellomo, Nicolas and Outada, Nisrine and Soler, Juan and Tao, Youshan and Winkler, Michael}}, journal = {{Mathematical Models & Methods in Applied Sciences}}, pages = {{713--792}}, title = {{{Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision.}}}, volume = {{32}}, year = {{2022}}, } @article{35530, author = {{Lankeit, Johannes and Winkler, Michael}}, journal = {{Journal of Evolution Equations}}, title = {{{Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptiva effects.}}}, volume = {{22}}, year = {{2022}}, } @article{35481, author = {{Fuhrmann, Jan and Lankeit, Johannes and Winkler, Michael}}, journal = {{Journal de Mathématiques Pures et Appliquées}}, pages = {{124--151}}, title = {{{A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system.}}}, volume = {{162}}, year = {{2022}}, } @article{35565, author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}}, journal = {{Acta Mathematica Sinica (English Series)}}, pages = {{985--1001}}, title = {{{A smallness condition ensuring boundedness in a two-dimensional chemotaxis-Navier-Stokes system involving Dirichlet boundary conditions for the signal.}}}, volume = {{38}}, year = {{2022}}, } @article{35560, author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}}, journal = {{Analysis and Applications}}, pages = {{141--170}}, title = {{{Global mass-preserving solutions to a chemotaxis-fluid model involving Dirichlet boundary conditions for the signal.}}}, volume = {{20}}, year = {{2022}}, } @article{40053, author = {{Graczyk, P. and Luks, Tomasz and Sawyer, P.}}, issn = {{0008-414X}}, journal = {{Canadian Journal of Mathematics}}, number = {{4}}, pages = {{1005--1033}}, publisher = {{Canadian Mathematical Society}}, title = {{{Potential kernels for radial Dunkl Laplacians}}}, doi = {{10.4153/s0008414x21000195}}, volume = {{74}}, year = {{2022}}, } @article{35556, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{Proceedings of the Royal Society of Edinburgh Section A: Mathematics}}, pages = {{81--101}}, title = {{{Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy.}}}, volume = {{152}}, year = {{2022}}, } @article{35532, author = {{Li, Genglin and Winkler, Michael}}, journal = {{Communications on Pure and Applied Analysis}}, pages = {{687--784}}, title = {{{Nonnegative solutions to a doubly degenerate nutrient taxis system }}}, volume = {{21}}, year = {{2022}}, } @article{34677, author = {{Black, Tobias and Wu, Chunyan}}, issn = {{0944-2669}}, journal = {{Calculus of Variations and Partial Differential Equations}}, keywords = {{Applied Mathematics, Analysis}}, number = {{3}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation}}}, doi = {{10.1007/s00526-022-02201-y}}, volume = {{61}}, year = {{2022}}, } @article{64570, author = {{Olbrich, Martin and Palmirotta, Guendalina}}, issn = {{0232-704X}}, journal = {{Annals of Global Analysis and Geometry}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces}}}, doi = {{10.1007/s10455-022-09882-w}}, volume = {{63}}, year = {{2022}}, } @article{64571, abstract = {{We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type $X = G/K$. We prove a characterisation of their range. In fact, from Delorme's Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections.}}, author = {{Olbrich, Martin and Palmirotta, Guendalina}}, journal = {{Journal of Lie theory}}, number = {{2}}, pages = {{53----384}}, publisher = {{Heldermann Verlag}}, title = {{{A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$}}}, volume = {{34}}, year = {{2022}}, } @article{51385, author = {{Hilgert, Joachim and Weich, Tobias and Bux, K.-U.}}, journal = {{J. of Spectral Theory}}, pages = {{659--681}}, title = {{{Poisson transforms for trees of bounded degree}}}, volume = {{12}}, year = {{2022}}, } @article{32016, author = {{Delarue, Benjamin and Ramacher, Pablo}}, journal = {{Journal of Symplectic Geometry}}, number = {{6}}, pages = {{1281 -- 1337}}, title = {{{Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}}}, doi = {{10.4310/JSG.2021.v19.n6.a1}}, volume = {{19}}, year = {{2021}}, } @article{34786, abstract = {{A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.}}, author = {{Glöckner, Helge and Willis, George A.}}, issn = {{0021-8693}}, journal = {{Journal of Algebra}}, keywords = {{Contraction group, Torsion group, Extension, Cocycle, Section, Equivariant cohomology, Abelian group, Nilpotent group, Isomorphism types}}, pages = {{164--214}}, title = {{{Decompositions of locally compact contraction groups, series and extensions}}}, doi = {{https://doi.org/10.1016/j.jalgebra.2020.11.007}}, volume = {{570}}, year = {{2021}}, } @article{34795, author = {{Glöckner, Helge}}, issn = {{0025-584X}}, journal = {{Mathematische Nachrichten}}, number = {{1}}, pages = {{74–81}}, title = {{{Direct limits of regular Lie groups}}}, doi = {{10.1002/mana.201900073}}, volume = {{294}}, year = {{2021}}, } @unpublished{34806, abstract = {{Let $G$ be a Lie group over a totally disconnected local field and $\alpha$ be an analytic endomorphism of $G$. The contraction group of $\alpha$ ist the set of all $x\in G$ such that $\alpha^n(x)\to e$ as $n\to\infty$. Call sequence $(x_{-n})_{n\geq 0}$ in $G$ an $\alpha$-regressive trajectory for $x\in G$ if $\alpha(x_{-n})=x_{-n+1}$ for all $n\geq 1$ and $x_0=x$. The anti-contraction group of $\alpha$ is the set of all $x\in G$ admitting an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $x_{-n}\to e$ as $n\to\infty$. The Levi subgroup is the set of all $x\in G$ whose $\alpha$-orbit is relatively compact, and such that $x$ admits an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $\{x_{-n}\colon n\geq 0\}$ is relatively compact. The big cell associated to $\alpha$ is the set $\Omega$ of all all products $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and $z$ in the anti-contraction group. Let $\pi$ be the mapping from the cartesian product of the contraction group, Levi subgroup and anti-contraction group to $\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\Omega$ is open in $G$ and $\pi$ is \'{e}tale for suitable immersed Lie subgroup structures on the three subgroups just mentioned. Moreover, we study group-theoretic properties of contraction groups and anti-contraction groups.}}, author = {{Glöckner, Helge}}, booktitle = {{arXiv:2101.02981}}, title = {{{Contraction groups and the big cell for endomorphisms of Lie groups over local fields}}}, year = {{2021}}, } @unpublished{31058, abstract = {{We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.}}, author = {{Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}}, title = {{{Resonances and weighted zeta functions for obstacle scattering via smooth models}}}, year = {{2021}}, }