@article{37672,
abstract = {{AbstractLet ${F}_{BC} (\lambda , k; t)$ be the Heckman–Opdam hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2} , {k}_{3} )$ and weighted half-sum $\rho (k)$ of positive roots. We prove that ${F}_{BC} (\lambda + \rho (k), k; t)$ converges as ${k}_{1} + {k}_{2} \rightarrow \infty $ and ${k}_{1} / {k}_{2} \rightarrow \infty $ to a function of type A for $t\in { \mathbb{R} }^{n} $ and $\lambda \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.}},
author = {{Rösler, Margit and Koornwinder, Tom and Voit, Michael}},
issn = {{0010-437X}},
journal = {{Compositio Mathematica}},
keywords = {{Algebra and Number Theory}},
number = {{8}},
pages = {{1381--1400}},
publisher = {{Wiley}},
title = {{{Limit transition between hypergeometric functions of type BC and type A}}},
doi = {{10.1112/s0010437x13007045}},
volume = {{149}},
year = {{2013}},
}
@article{38038,
author = {{Rösler, Margit and Voit, Michael}},
journal = {{Journal of Lie Theory 23}},
number = {{4}},
pages = {{899----920}},
publisher = {{Heldermann }},
title = {{{Olshanski spherical functions for infinite dimensional motion groups of fixed rank}}},
doi = {{10.48550/ARXIV.1210.1351}},
year = {{2013}},
}
@article{40072,
author = {{Luks, Tomasz}},
issn = {{0926-2601}},
journal = {{Potential Analysis}},
number = {{1}},
pages = {{29--67}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane}}},
doi = {{10.1007/s11118-012-9321-x}},
volume = {{39}},
year = {{2013}},
}
@article{40070,
author = {{Graczyk, Piotr and Jakubowski, Tomasz and Luks, Tomasz}},
issn = {{1385-1292}},
journal = {{Positivity}},
number = {{4}},
pages = {{1043--1070}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation}}},
doi = {{10.1007/s11117-012-0220-6}},
volume = {{17}},
year = {{2013}},
}
@inbook{64731,
author = {{Glöckner, Helge}},
booktitle = {{Advances in Ultrametric Analysis. 12th International Conference p-Adic Functional Analysis, University of Manitoba, Winnipeg, Canada, July 2-6, 2012}},
title = {{{Grobman-Hartman Theorems for Diffeomorphisms of Banach Spaces over Valued Fields}}},
year = {{2013}},
}
@phdthesis{64748,
author = {{Alzaareer, Hamza}},
title = {{{Lie groups of mappings on non-compact spaces and manifolds}}},
year = {{2013}},
}
@phdthesis{64750,
author = {{Schmeding, Alexander}},
title = {{{The diffeomorphism group of a non-compact orbifold}}},
year = {{2013}},
}
@unpublished{64744,
author = {{Glöckner, Helge}},
title = {{{Differentiable mappings between spaces of sections}}},
year = {{2013}},
}
@unpublished{64763,
author = {{Schütt, Jakob}},
title = {{{Symmetry Groups of Principal Bundles Over Non-Compact Bases}}},
year = {{2013}},
}
@article{64669,
author = {{Glöckner, Helge}},
issn = {{2156-2261}},
journal = {{Kyoto Journal of Mathematics}},
keywords = {{22E45, 22D12, 46A13, 46E25, 46F05}},
number = {{3}},
pages = {{567–595}},
title = {{{Continuity of LF-algebra representations associated to representations of Lie groups}}},
doi = {{10.1215/21562261-2265895}},
volume = {{53}},
year = {{2013}},
}
@article{64670,
author = {{Glöckner, Helge}},
issn = {{0723-0869}},
journal = {{Expositiones Mathematicae}},
keywords = {{37D10, 46S10, 26E30, 22E20, 37P20}},
number = {{2}},
pages = {{116–150}},
title = {{{Invariant manifolds for analytic dynamical systems over ultrametric fields}}},
doi = {{10.1016/j.exmath.2013.01.009}},
volume = {{31}},
year = {{2013}},
}
@article{64668,
author = {{Glöckner, Helge}},
issn = {{2070-0466}},
journal = {{p-Adic Numbers, Ultrametric Analysis and Applications}},
keywords = {{26E30, 12J25}},
number = {{2}},
pages = {{122–159}},
title = {{{Exponential laws for ultrametric partially differentiable functions and applications}}},
doi = {{10.1134/S2070046613020039}},
volume = {{5}},
year = {{2013}},
}
@article{31300,
author = {{Potzuweit, A. and Weich, Tobias and Barkhofen, Sonja and Kuhl, U. and Stöckmann, H.-J. and Zworski, M.}},
issn = {{1539-3755}},
journal = {{Physical Review E}},
keywords = {{Industrial and Manufacturing Engineering, Metals and Alloys, Strategy and Management, Mechanical Engineering}},
number = {{6}},
publisher = {{American Physical Society (APS)}},
title = {{{Weyl asymptotics: From closed to open systems}}},
doi = {{10.1103/physreve.86.066205}},
volume = {{86}},
year = {{2012}},
}
@article{51396,
author = {{Hilgert, Joachim and Orsted, B. and Möllers, J. and Kobayashi, T.}},
journal = {{J. Funct. Anal.}},
pages = {{3492--3563}},
title = {{{Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups}}},
volume = {{263}},
year = {{2012}},
}
@article{51397,
author = {{Hilgert, Joachim and Palzer, W. and Alldridge, A.}},
journal = {{Journal of Geometry and Physics}},
pages = {{427--448}},
title = {{{Integration on non-compact supermanifolds}}},
volume = {{62}},
year = {{2012}},
}
@article{51398,
author = {{Hilgert, Joachim and Schröder, M. and Hansen, S.}},
journal = {{Math. Z.}},
pages = {{607--643}},
title = {{{Patterson-Sullivan distributions in higher rank}}},
volume = {{272}},
year = {{2012}},
}
@book{51492,
author = {{Hilgert, Joachim and Hilgert, Ingrid}},
publisher = {{Springer Spektrum}},
title = {{{Mathematik - Ein Reiseführer}}},
year = {{2012}},
}
@unpublished{64740,
author = {{Glöckner, Helge}},
title = {{{Regularity properties of infinite-dimensional Lie groups, and semiregularity}}},
year = {{2012}},
}
@article{64754,
author = {{Walter, Boris}},
issn = {{0012-3862}},
journal = {{Dissertationes Mathematicae}},
keywords = {{58D05, 22E65, 22E67, 26E15, 26E20, 46E10, 46E40, 46E50, 46T05, 46T10, 46T20, 58D15}},
pages = {{126}},
title = {{{Weighted diffeomorphism groups of Banach spaces and weighted mapping groups}}},
doi = {{10.4064/dm484-0-1}},
volume = {{484}},
year = {{2012}},
}
@article{64672,
author = {{Glöckner, Helge}},
issn = {{0166-8641}},
journal = {{Topology and its Applications}},
keywords = {{46A03, 46F05, 22D15, 42A85, 46A11, 46A32}},
number = {{13}},
pages = {{2990–3001}},
title = {{{Upper bounds for continuous seminorms and special properties of bilinear maps}}},
doi = {{10.1016/j.topol.2012.05.010}},
volume = {{159}},
year = {{2012}},
}