On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows - Weich, Tobias (Annales Henri Poincaré)
Keywords: Mathematical Physics; Nuclear and High Energy Physics; Statistical and Nonlinear Physics

Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC - Rösler, Margit; Voit, Michael (Transactions of the American Mathematical Society)

A multivariate version of the disk convolution - Rösler, Margit; Voit, Michael (Journal of Mathematical Analysis and Applications)
Keywords: Applied Mathematics; Analysis

Hardy–Stein identities and square functions for semigroups - Bañuelos, Rodrigo; Bogdan, Krzysztof; Luks, Tomasz (Journal of the London Mathematical Society)
Keywords: General Mathematics

Schwierigkeiten beim Übergang von Schule zu Hochschule im zeitlichen Vergleich - Ein Blick auf Defizite beim Erwerb von Schlüsselkompetenzen - Hilgert, Joachim (Lehren und Lernen von Mathematik in der Studieneingangsphase)

Resonances for the Laplacian: the cases BC2 and C2 (except SO(p,2) with p>2 odd) - Hilgert, Joachim; Pasquale, A.; Przebinda, T. (Geometric Methods in Physics)

Mathematische Strukturen

Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps - ARNOLDI, JEAN FRANCOIS; FAURE, FRÉDÉRIC; Weich, Tobias (Ergodic Theory and Dynamical Systems)
We consider a simple model of an open partially expanding map. Its trapped set ${\mathcal{K}}$ in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component $\unicode[STIX]{x1D708}$ in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of ${\mathcal{K}}$ . Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit $\unicode[STIX]{x1D708}→ ∞$ . Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results.
Keywords: Applied Mathematics; General Mathematics

Resonance Chains and Geometric Limits on Schottky Surfaces - Weich, Tobias (Communications in Mathematical Physics)
Keywords: Mathematical Physics; Statistical and Nonlinear Physics

A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian - Rösler, Margit; Voit, Michael (Symmetry, Integrability and Geometry: Methods and Applications)
Keywords: Geometry and Topology; Mathematical Physics; Analysis

Kann professorale Lehre tutoriell sein? Ein Modellversuch zur Einführung in mathematisches Denken und Arbeiten - Hilgert, Joachim; Hoffmann, Max; Panse, Anja (Tagungsband zum Hansekolloquium zur Hochschuldidaktik der Mathematik.)

Einführung in mathematisches Denken und Arbeiten: tutoriell und transparent - Hilgert, Joachim; Hoffmann, Max; Panse, Anja

Resonances for the Laplacian: the cases BC2 and C2 (except over SOo(p,2), p>0 odd) - Hilgert, Joachim; Pasquale, A.; Przebinda, T.

Contraction of Hamiltonian K-spaces - Hilgert, Joachim; Manon, C.; Martens, J.

Resonances for the Laplacian of products of two rank one Riemannian symmetric spaces - Hilgert, Joachim; Pasquale, A.; Przebinda, T.

Superorbits - Hilgert, Joachim; Alldridge, A.; Wurzbacher, T.

Equivariant spectral asymptotics forh-pseudodifferential operators - Weich, Tobias (Journal of Mathematical Physics)
Keywords: Mathematical Physics; Statistical and Nonlinear Physics

Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum - Barkhofen, Sonja; Faure, F; Weich, Tobias (Nonlinearity)
Keywords: Applied Mathematics; General Physics and Astronomy; Mathematical Physics; Statistical and Nonlinear Physics

Formation and interaction of resonance chains in the open three-disk system - Weich, Tobias; Barkhofen, Sonja; Kuhl, U; Poli, C; Schomerus, H (New Journal of Physics)
Keywords: General Physics and Astronomy

Convolution algebras for Heckman–Opdam polynomials derived from compact Grassmannians - Rösler, Margit; Remling, Heiko (Journal of Approximation Theory)
Keywords: Applied Mathematics; General Mathematics; Numerical Analysis; Analysis

On Hardy spaces of local and nonlocal operators - Bogdan, Krzysztof; Dyda, Bartłomiej; Luks, Tomasz (Hiroshima Mathematical Journal)

Handlungsbedarf in fachmathematischen Veranstaltungen? – Spezielle Maßnahmen an der Universität Paderborn - Panse, Anja; Hilgert, Joachim; Hoffmann, Max (Beiträge zum Mathematikunterricht 2014)

Minimal representations via Bessel operators - Hilgert, Joachim; Möllers, J.; Kobayashi, T. (J. Math. Soc. Japan)

Singular superspaces - Hilgert, Joachim; Wurzbacher, T.; Alldridge, A. (Math. Z.)

The Radon transform and its dual for limits of symmetric spaces - Hilgert, Joachim; Ólafsson, G. (Developments and Retrospectives in Lie Theory - Geometric and Analytic Methods)

Schwierigkeiten von Studienanfängern, verschiedene Lehrmethoden und Fragen an die Didaktik - Hilgert, Joachim; Hoffmann, M.; Panse, A. (Beiträge zum Mathematikunterricht 2014)

Resonances for the Laplacian on Riemannian symmetric spaces: the case of SL(3,R)/SO(3) - Hilgert, Joachim; Pasquale, A.; Przebinda, T.

Discontinuity of the Fuglede-Kadison determinant on a group von Neumann algebra - Küster, Benjamin (Communications in Mathematics)

Experimental Observation of the Spectral Gap in Microwave n-Disk Systems - Barkhofen, Sonja; Weich, Tobias; Potzuweit, A.; Stöckmann, H.-J.; Kuhl, U.; Zworski, M. (Physical Review Letters)
Keywords: General Physics and Astronomy

Limit transition between hypergeometric functions of type BC and type A - Rösler, Margit; Koornwinder, Tom; Voit, Michael (Compositio Mathematica)
Abstract Let ${F}_{BC} (λ , k; t)$ be the Heckman–Opdam hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2} , {k}_{3} )$ and weighted half-sum $ρ (k)$ of positive roots. We prove that ${F}_{BC} (λ + ρ (k), k; t)$ converges as ${k}_{1} + {k}_{2} → ∞ $ and ${k}_{1} / {k}_{2} → ∞ $ to a function of type A for $t\in { \mathbb{R} }^{n} $ and $λ \in { \mathbb{C} }^{n} $ . This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more general limit behavior of the multiplicities, using an explicit representation of Jacobi polynomials in terms of Jack polynomials. Our limits include limit transitions for the spherical functions of non-compact Grassmann manifolds over one of the fields $ \mathbb{F} = \mathbb{R} , \mathbb{C} , \mathbb{H} $ when the rank is fixed and the dimension tends to infinity. The limit functions turn out to be exactly the spherical functions of the corresponding infinite-dimensional Grassmann manifold in the sense of Olshanski.
Keywords: Algebra and Number Theory

Olshanski spherical functions for infinite dimensional motion groups of fixed rank - Rösler, Margit; Voit, Michael (Journal of Lie Theory 23)

Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane - Luks, Tomasz (Potential Analysis)

Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation - Graczyk, Piotr; Jakubowski, Tomasz; Luks, Tomasz (Positivity)

Harmonic analysis on Heisenberg-Clifford Lie supergroups - Hilgert, Joachim; Laubinger, M.; Alldridge, A. (J. London Math. Soc.)

Arbeitsbuch Mathematik für das erste Studienjahr

Lesebuch Mathematik für das erste Studienjahr

The Radon transform and its dual for limits of symmetric spaces - Hilgert, Joachim; Ólafsson, G.

Singular superspaces - Hilgert, Joachim; Alldridge, A.; Wurzbacher, T.

Weyl asymptotics: From closed to open systems - Potzuweit, A.; Weich, Tobias; Barkhofen, Sonja; Kuhl, U.; Stöckmann, H.-J.; Zworski, M. (Physical Review E)
Keywords: Industrial and Manufacturing Engineering; Metals and Alloys; Strategy and Management; Mechanical Engineering

Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups - Hilgert, Joachim; Orsted, B.; Möllers, J.; Kobayashi, T. (J. Funct. Anal.)

Integration on non-compact supermanifolds - Hilgert, Joachim; Palzer, W.; Alldridge, A. (Journal of Geometry and Physics)

Patterson-Sullivan distributions in higher rank - Hilgert, Joachim; Schröder, M.; Hansen, S. (Math. Z.)

Mathematik - Ein Reiseführer

Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups - Hilgert, Joachim; Kobayashi, T.; Möllers, J.; Orsted, B.

Hardy spaces for the Laplacian with lower order perturbations - Luks, Tomasz (Studia Mathematica)

The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann Transform - Rösler, Margit; Remling, H. (International Mathematics Research Notices)
Keywords: General Mathematics

Limit theorems for radial random walks on p × q-matrices as p tends to infinity - Rösler, Margit; Voit, Michael (Mathematische Nachrichten)
Keywords: General Mathematics

Orthogonal polynomials associated to a certain fourth order differential equation - Hilgert, Joachim; Möllers, J.; Mano, G.; Kobayashi, T. (Ramanujan J.)

Special functions associated to a certain fourth order differential equation - Hilgert, Joachim; Möllers, J.; Mano, G.; Kobayashi, T. (Ramanujan J.)

An Introduction to the Structure and Geometry of Lie Groups

Minimal representations via Bessel operators - Hilgert, Joachim; Kobayashi, T.; Möllers, J.

Harmonic analysis on Heisenberg--Clifford Lie supergroups - Hilgert, Joachim; Alldridge, A.; Laubinger, M.

Patterson--Sullivan distributions in higher rank - Hilgert, Joachim; Hansen, S.; Schröder, M.

Integration on Non-Compact Supermanifolds - Hilgert, Joachim; Alldridge, A.; Palzer, W.

Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC - Rösler, Margit (Journal of Functional Analysis)
Keywords: Analysis

Chevalley's Restriction Theorem for Reductive Symmetric Superpairs - Hilgert, Joachim; Zirnbauer, M.; Alldridge, A. (J. Algebra)

Invariant Berezin integration on homogeneous supermanifolds - Hilgert, Joachim; Alldridge, A. (J. Lie Theory)

Convolution algebras for multivariable Bessel functions - Rösler, Margit (Infinite Dimensional Harmonic Analysis IV)

Resonances and Residue Operators for Symmetric Spaces of Rank One - Hilgert, Joachim; Pasquale, A. (J. Math. Pures Appl.)

Asymptotic K-support and Restrictions of Representations - Hilgert, Joachim; Keliny, S.; Hansen, S. (Representation Theory)

Segal-Bargmann and Weyl Transforms on Compact Groups - Hilgert, Joachim; Zhang, G. (Monatsh. Math.)

Symbolic Dynamics for the Geodesic Flow on Locally Symmetric Orbifolds of Rank One - Hilgert, Joachim; Pohl, A. (Infinite Dimensional Harmonic Analysis IV)

Orthogonal polynomials associated to a certain fourth order differential equation - Hilgert, Joachim; Kobayashi, T.; Mano, G.; Möllers, J.

Special functions associated to a certain fourth order differential equation - Hilgert, Joachim; Kobayashi, T.; Mano, G.; Möllers, J.

Patterson--Sullivan distributions for rank one symmetric spaces of the noncompact type - Hilgert, Joachim; Schröder, M.

Invariant Berezin integration on homogeneous supermanifolds - Hilgert, Joachim; Alldridge, A.

Asymptotic K-Support and Restrictions of Representations - Hilgert, Joachim; Hansen, S.; Keliny, S.

Infinite Dimensional Harmonic Analysis IV - On the Interplay between Representation Theory, Random Matrices, Special Functions, and Probability

A Limit Relation for Dunkl-Bessel Functions of Type A and B - Rösler, Margit; Voit, Michael (Symmetry, Integrability and Geometry: Methods and Applications)
Keywords: Geometry and Topology; Mathematical Physics; Analysis

Meromorphic Continuation of Dynamical Zeta Functions via Transfer Operators - Hilgert, Joachim; Rilke, F. (J. Funct. Anal.)

Mayer's Transfer Operator and Representations of SL(2) - Hilgert, Joachim (Semigroup Forum)

Symbolic dynamics for the geodesic flow on locally symmetric orbifolds of rank one - Hilgert, Joachim; Pohl , A. D.

Chevalley's restriction theorem for reductive symmetric superpairs - Hilgert, Joachim; Alldridge, A.; Zirnbauer, M.

Attractor Networks on Complex Flag Manifolds - Hilgert, Joachim

Faraut, J. Analysis on Lie Groups (Cambridge University Press, 2008) - Hilgert, Joachim (Math. Reviews)

Bessel convolutions on matrix cones - Rösler, Margit (Compositio Mathematica)
Keywords: Algebra and Number Theory

The Lewis Correspondence for Submodular Groups - Hilgert, Joachim; Deitmar, A. (Forum Math.)

Meromorphic continuation of dynamical zeta functions via transfer operators - Hilgert, Joachim; Rilke, F.

Wolf, J..A. Harmonic Analysis on Commutative Spaces (AMS, 2007) - Hilgert, Joachim (Math. Reviews)

Procesi, C. Lie Groups (Springer, 2007) - Hilgert, Joachim (JBer. DMV)

SU(d)-Biinvariant Random Walks on SL(d,C) and their Euclidean Counterparts - Rösler, Margit; Voit, Michael (Acta Applicandae Mathematicae)
Keywords: Applied Mathematics

Adler, M., P. Moerbeke, P. Vanhaecke. Algebraic integrability, Painlevé geometry and Lie algebras (Springer, 2004) - Hilgert, Joachim (JBer. DMV)

Stroppel, M. Topological groups (EMS, 2006) - Hilgert, Joachim (Zentralblatt für Math.)

Radial Multiresolution in Dimension Three - Rösler, Margit; Rauhut, Holger (Constructive Approximation)
Keywords: Computational Mathematics; General Mathematics; Analysis

Deformations of convolution semigroups on commutative hypergroups - Rösler, Margit; VOIT, MICHAEL (Infinite Dimensional Harmonic Analysis III)

An Ergodic Arnold-Liouville Theorem for Symmetric Spaces - Hilgert, Joachim (Twenty Years of Bialowieza: A Mathematical Antology)

Transfer Operators for Gamma_0(n) and the Hecke Operators for the Period Functions of PSL(2,Z) - Hilgert, Joachim; Movasati, H.; Mayer, D. (Math. Proc. Camb. Phil. Soc.)

Dungey, N., A. ter Elst, D. Robinson. Analysis on Lie Groups with Polynomial Growth (Birkhäuser, Boston, 2003) - Hilgert, Joachim (JBer. DMV)

Cohomology of Arithmetic Groups with Infinite Dimensional Coefficient Spaces - Hilgert, Joachim; Deitmar, A. (Documanta Math.)

Positivity of Dunkl's intertwining operator via the trigonometric setting - Rösler, Margit; Voit, Michael (International Mathematics Research Notices)
In this note, a new proof for the positivity of Dunkl's intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their non-symmetric counterparts.

The Dynamical Zeta Function and Transfer Operators for the Kac-Baker Model - Hilgert, Joachim; Mayer, D. (Complex Analysis and Dynamical Systems)

The Lewis Correspondence for submodular groups - Hilgert, Joachim; Deitmar, A.

Dunkl Operators: Theory and Applications - Rösler, Margit (Lecture Notes in Mathematics)

A positive radial product formula for the Dunkl kernel - Rösler, Margit (Transactions of the American Mathematical Society)
It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radial hereby means that one of the factors in the product formula is replaced by its mean over a sphere. The key to this product formula is a positivity result for the Dunkl-type spherical mean operator. It can also be interpreted in the sense that the Dunkl-type generalized translation of radial functions is positivity-preserving. As an application, we construct Dunkl-type homogeneous Markov processes associated with radial probability distributions.

The Dual Horospherical Radon Transform as a Limit of Spherical Radon Transforms - Hilgert, Joachim; Vinberg, E.B.; Pasquale, A. (AMS Translations)

Transfer operators for Γ0(n) and the Hecke operators for the period functions for PSL(2,Z) - Hilgert, Joachim; Mayer, D.; Movasati, H.

Cohomology of arithmetic groups with infinite dimensional coefficient spaces - Hilgert, Joachim; Deitmar, A.

Asymptotic Analysis for the Dunkl Kernel - Rösler, Margit; de Jeu, Marcel (Journal of Approximation Theory)
Keywords: Applied Mathematics; General Mathematics; Numerical Analysis; Analysis

Representation Theory of Lie Groups - Hilgert, Joachim (Handbook on the Heart of Algebra)

Lie Groups - Hilgert, Joachim (Handbook on the Heart of Algebra)