Helge Glöckner's Publications and Preprints

Total number of publications (excluding preprints and theses): 87

Articles in refereed mathematical journals:

  1. Deep neural networks on diffeomorphism groups for optimal shape reparameterization (with E. Celledoni, J. Riseth, and A. Schmeding), to appear in BIT Numerical Mathematics (cf. arXiv:2207.11141)
  2. Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups (with L. Tárrega), J. Lie Theory 33 (2023), 271-296.
  3. Diffeomorphism groups of convex polytopes, J. Convex Anal. 30 (2023), 343-358.
  4. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds (with J. Hilgert), J. Differ. Equations 343 (2023), 186-232.
  5. Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces, Axioms 11 (2022), no. 5, article 221 (open access)
  6. Non-Lie subgroups in Lie groups over local fields of positive characteristic, p-Adic Numbers Ultrametric Anal. Appl. 14 (2022), no. 2, 138-144.
  7. Manifolds of mappings on Cartesian products (with A. Schmeding), Ann. Global Anal. Geom. 61 (2022), 359-398.
  8. Locally pro-p contraction groups are nilpotent (with G.A. Willis), J. Reine Angew. Math. 781 (2021), 85-103.
  9. Decompositions of locally compact contraction groups, series and extensions (with G.A. Willis), J. Algebra 570 (2021), 164-214.
  10. Direct limits of regular Lie groups, Math. Nachr. 294 (2021), no. 1, 74-81.
  11. Lie groupoids of mappings taking values in a Lie groupoid (with H. Amiri and A. Schmeding), Arxivum Math. 56 (2020), no. 5, 307-356.
  12. Products of regular locally compact spaces are kR-spaces (with N. Masbough), Top. Proc. 55 (2020), 35-38.
  13. Completeness of infinite-dimensional Lie groups in their left uniformity, Canadian J. Math. 71 (2019), no. 1, 131-152.
  14. Contraction groups and passage to subgroups and quotients for endomorphisms of totally disconnected locally compact groups (with T. P. Bywaters and S. Tornier), Israel J. Math. 227 (2018), 691-752.
  15. Completeness of locally komega-groups and related infinite-dimensional Lie groups, Topol. Appl. 228 (2017), 277-284.
  16. Diffeomorphism groups of compact convex sets (with Karl-Hermann Neeb), Indag. Math. 28 (2017), 760--783.
  17. Elementary p-adic Lie groups have finite construction rank, Proc. Amer. Math. Soc. 145 (2017), no. 11, 5007-5021.
  18. Expansive automorphisms of totally disconnected, locally compact groups (with C.R.E. Raja), J. Group Theory 20 (2017), no. 3, 589-619.
  19. Homotopy groups of ascending unions of infinite-dimensional manifolds, to appear in Ann. Inst. Fourier (Grenoble) (cf. arXiv:0812.4713v2)
  20. The kernel of the adjoint representation of a p-adic Lie group need not have an abelian open normal subgroup, Commun. Algebra 44 (2016), no. 7, 2981-2988.
  21. Bounded solutions of finite lifetime to differential equations in Banach spaces (with R. Dahmen), Acta Sci. Math. (Szeged) 81 (2015), 457-468.
  22. Weighted inversion of general Dirichlet series (with L.G. Lucht), Trans. Amer. Math. Soc. 366 (2014), no. 6, 3275-3293.
  23. Continuity of convolution of test functions on Lie groups (with L. Birth), Canadian J. Math. 66 (2014), no. 1, 102-140.
  24. Exponential laws for ultrametric partially differentiable functions and applications, p-Adic Numbers Ultram. Anal. Appl. 5 (2013), no. 2, 122-159.
  25. Continuity of LF-algebra representations associated to representations of Lie groups, Kyoto J. Math. 53 (2013), no. 3, 567-595.
  26. Invariant manifolds for analytic dynamical systems over ultrametric fields, Expo. Math. 31 (2013), 116-150.
  27. When unit groups of continuous inverse algebras are regular Lie groups (with K.-H. Neeb), Studia Math. 211 (2012), 95-109.
  28. Upper bounds for continuous seminorms and special properties of bilinear maps, Topol. Appl. 159 (2012), 2990-3001.
  29. Continuity of bilinear maps on direct sums of topological vector spaces, J. Funct. Anal. 262 (2012), no. 5, 2013-2030.
  30. Topological algebras of rapidly decreasing matrices and generalizations (with B. Langkamp), Topol. Appl. 159 (2012), 2420-2422.
  31. Classification of the simple factors appearing in composition series of totally disconnected contraction groups (with G.A. Willis), J. Reine Angew. Math. 634 (2010), 141-169.
  32. Final group topologies, Kac-Moody groups and Pontryagin duality (with R. Gramlich and T. Hartnick), Israel J. Math. 177 (2010), 49-102.
  33. General Dirichlet series, arithmetic convolution equations and Laplace transforms (with L.G. Lucht and S. Porubsky), Stud. Math. 193 (2009), no. 2, 109-129.
  34. Solutions to open problems in Neeb's recent survey on infinite-dimensional Lie groups, Geom. Dedicata 135 (2008), 71-86.
  35. Contractible Lie groups over local fields, Math. Z. 260 (2008), 889-904
  36. Ultrametric and non-locally convex analogues of the general curve lemma of convenient differential calculus, Glasgow Math. J. 50 (2008), no. 2, 271-288.
  37. Comparison of some notions of C^k-maps in multi-variable non-archimedian analysis, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 877-904.
  38. Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories, J. Funct. Anal. 245 (2007), 19-61.
  39. Direct limit groups do not have small subgroups, Topol. Appl. 154 (2007), 1126-1133.
  40. Solutions to arithmetic convolution equations (with L.G. Lucht and S. Porubsky), Proc. Amer. Math. Soc. 135 (2007), 1619-1629.
  41. Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms (with G.A. Willis), Topology Proceedings 31 (2007), 481-501.
  42. Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces, J. Math. Kyoto Univ. 47 (2007), 631-642.
  43. Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma, J. Lie Theory 17 (2007), 899-902.
  44. Implicit functions from topological vector spaces to Banach spaces, Israel J. Math. 155 (2006), 205-252.
  45. Every smooth p-adic Lie group admits a compatible analytic structure, Forum Math. 18 (2006), 45-84.
  46. Locally compact groups built up from p-adic Lie groups, for p in a given set of primes, J. Group Theory 9 (2006), no. 4, 427-454.
  47. Fundamental problems in the theory of infinite-dimensional Lie groups, J. Geom. Symm. Phys. 5 (2006), 24-35.
  48. Discontinuous non-linear mappings on locally convex direct limits, Publ. Math. Debrecen 68/1-2 (2006), 1-13
  49. Hölder continuous homomorphisms between infinite-dimensional Lie groups are smooth, J. Funct. Analysis 228 (2005), no. 2, 419-444.
  50. Conveniently Hölder homomorphisms are smooth in the convenient sense, Ann. Global Anal. Geom. 27 (2005), 227-255.
  51. Fundamentals of direct limit Lie theory, Compositio Math. 141 (2005), 1551-1577.
  52. Smooth Lie groups over local fields of positive characteristic need not be analytic, J. Algebra 285 (2005), 356-371.
  53. Diff(R^n) as a Milnor-Lie group, Math. Nachr. 278 (2005), No. 9, 1025-1032.
  54. Contraction groups for tidy automorphisms of totally disconnected groups, Glasgow Math. J. 47 (2005), no. 2, 329-333.
  55. Differential calculus over general base fields and rings (with W. Bertram and K.-H. Neeb), Expo. Math. 22 (2004), 213-282.
  56. Tensor products in the category of topological vector spaces are not associative, Comment. Math. Univ. Carol. 45 (2004), no. 4, 607-614.
  57. Examples of differentiable mappings into non-locally convex spaces, Topol. Proc. 28 (2004), No. 2, 479-486.
  58. Positive definite functions on infinite-dimensional convex cones, Memoirs Amer. Math. Soc. 789 (2003), xiv+128 pp
  59. Banach-Lie quotients, enlargibility, and universal complexifications (with K.-H. Neeb), J. Reine Ang. Math. 560 (2003), 1-28.
  60. Direct limit Lie groups and manifolds, J. Math. Kyoto Univ. 43 (2003), 1- 26.
  61. Lie groups of measurable mappings, Canadian J. Math. 55 (2003), no. 5, 969-999.
  62. Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups, J. Funct. Analysis 194 (2002), No. 2, 347-409.
  63. Algebras whose groups of units are Lie groups, Studia Math. 153 (2002), 147-177.
  64. Topologization of Hecke pairs and Hecke C*-algebras (with G.A. Willis), Topol. Proc. 26 (2001-2002), No. 2, 565-591.
  65. Approximation by p-adic Lie groups, Glasgow Math. J. 44 (2002), 231-239.
  66. Real and p-adic Lie algebra functors on the category of topological groups, Pacific J. Math. 203 (2002), No. 2, 321-368.
  67. Uniscalar p-adic Lie groups (with G. A. Willis), Forum Math. 13 (2001), 413-421.
  68. Functions operating on positive semidefinite quaternionic matrices, Monatsh. Math. 132 (2001), No.4, 303-324.
  69. Representations of cones and conelike semigroups, Semigroup Forum 60 (2000), 326-333.
  70. Scale functions on p-adic Lie groups, Manuscr. Math. 97 (1998), 205-215.
  71. Scale functions on linear groups over local skew fields, J. Algebra 205 (1998), 525-541.
  72. Haar measure on linear groups over local skew fields, J. Lie Theory 6 (1996), 165-177.

Articles in refereed conference proceedings:

  1. Endomorphisms of Lie groups over local fields, pp. 101-165 in: "2016 MATRIX Annals," Springer-Verlag, Cham, 2018.
  2. Lectures on Lie groups over local fields, pp. 37-72 in: P.-E. Caprace and N. Monod (eds.), "New Directions in Locally Compact Groups," London Math. Soc. Lect. Note Series 447, Cambridge University Press, 2018.
  3. Invariant manifolds for finite-dimensional non-archimedean dynamical systems, pp. 73-90 in: H. Glöckner, A. Escassut, and K. Shamseddine (eds.), ``Advances in Non-Archimedean Analysis,'' AMS, Contemp. Math. 665, 2016.
  4. Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields, pp. 79-101 in: K. Shamseddine (ed.), "Advances in Ultrametric Analysis," Contemp. Math. 596, AMS, 2013.
  5. Direct limits of infinite-dimensional Lie groups, pp. 243-280 in: K.-H. Neeb and A. Pianzola (eds), ``Developments and Trends in Infinite-Dimensional Lie Theory,'' Birkhäuser, Progr. Math. 288, 2011.
  6. Applications of hypocontinuous bilinear maps in infinite-dimensional differential calculus, pp. 171-186 in: S. Silvestrov, E. Paal, V. Abramov and A. Stolin (eds.), ``Generalized Lie Theory in Mathematics, Physics and Beyond,'' Springer Verlag, 2008.
  7. Lie groups of germs of analytic mappings, pp 1-16 in: Turaev, V. and T. Wurzbacher (Eds.), ``Infinite dimensional groups and manifolds,'' IRMA Lecture Notes in Mathematics and Theoretical Physics, de Gruyter, 2004.
  8. Infinite-dimensional Lie groups without completeness restrictions, pp. 43-59 in: Strasburger, A. et al. (Eds.), ``Geometry and Analysis on Finite- and Infinite-Dimensional Lie Groups,'' Banach Center Publications, Vol. 55, Warsaw, 2002.
  9. A property of locally compact groups (with J. Winkelmann), pp. 205-210 in: Bajo, I., and E. Sanmartin (Eds.), ``Recent Advances in Lie Theory,'' Research and Exposition in Mathematics 25, Heldermann-Verlag, Berlin, 2002.
  10. Minimally almost periodic abelian groups and commutative W*-algebras (with K.-H. Neeb), pp. 163-186 in: Martín Peinador, E. and J. Nunez Garcia (Eds.), ``Nuclear Groups and Lie Groups,'' Research and Exposition in Mathematics 24, Heldermann-Verlag, Berlin, 2001.

Articles in non-refereed conference proceedings:

  1. Regularity properties of infinite-dimensional Lie groups, Oberwolfach Rep. 13 (2013), 791-794.
  2. Homotopy groups of topological spaces containing a dense directed union of manifolds, Oberwolfach Rep. 7 (2010), no. 4, 3037-3039
  3. Direct limits of infinite-dimensional Lie groups, Oberwolfach Rep. 3 (2006), no. 4, 3286-3289
  4. Aspects of p-adic non-linear functional analysis, pp. 237-253 in: A. Yu. Krennikov, Z. Rakic and I. V. Volovich (Eds), p-Adic Mathematical Physics. 2nd International Conference (Belgrade, 2005), AIP conference proceedings 826, Amer. Inst. Physics, New York, 2006.
  5. Direct limits of Lie groups, Oberwolfach Rep. 1 (2004), no. 1, 321-324.

Books edited

  1. H. Glöckner, A. Escassut, and K. Shamseddine (eds.), ``Advances in Non-Archimedean Analysis,'' AMS, Contemp. Math. 665, 2016, 335 pp.

Preprints and submitted articles:

  1. Birkhoff decompositions for loop groups with coefficient algebras, preprint, 28 pp, June 2022; arXiv:2206.11711
  2. Contraction groups and the big cell for endomorphisms of Lie groups over local fields, preprint, 34 pp, January 2021; arXiv:2101.02981
  3. Diffeomorphism groups of real analytic manifolds are L^1-regular, preprint, 47 pp, September 2023 (first version July 2020); arXiv:2007.15611
  4. Smoothing operators for vector-valued functions and extension operators, preprint, 118 pp, May 2020; arXiv:2006.00254
  5. Measurable regularity properties of infinite-dimensional Lie groups, preprint, 229 pp, December 2015; arXiv:1601.02568
  6. Fundamentals of submersions and immersions between infinite-dimensional manifolds, preprint, 39 pp, October 2016 (first version: February 2015); arXiv:1502.05795
  7. Complexifications of infinite-dimensional manifolds and new constructions of infinite-dimensional Lie groups (with R. Dahmen and A. Schmeding), preprint, 32 pp, October 2014; arXiv:1410.6468
  8. Regularity properties of infinite-dimensional Lie groups and semiregularity, preprint, 68 pp, February 2016 (first version: August 2012), arXiv:1208.0715
  9. Finite order differentiability properties, fixed points and implicit functions over valued fields, preprint, 59 pp, April 2007 (earlier version: 56 pp, November 2005); math/0511218
  10. Implicit functions from topological vector spaces to Frechet spaces in the presence of metric estimates, preprint, 51 pp, December 2006; math/0612673
  11. Lie groups over non-discrete topological fields, preprint, 128 pp, August 2004; math/0408008
  12. Patched locally convex spaces, almost local mappings, and diffeomorphism groups of non-compact manifolds, manuscript.
  13. Differentiable mappings between spaces of sections, manuscript, 2002, 30 pp. (now a preprint: arXiv:1308.1172)

Theses:

  1. Zum Isomorphieproblem linearer Gruppen über lokalen Körpern, Diplomarbeit, TH Darmstadt, 1995 (Advisor: M. Stroppel).
  2. Infinite-Dimensional Complex Groups and Semigroups: Representations of Cones, Tubes, and Conelike Semigroups, xviii+300 pp, Doktorarbeit, TU Darmstadt, 2000 (Advisor: K.-H. Neeb).
  3. Extending the Scope of Lie Theory to Larger Classes of Groups, 405 pp, Habilitationsschrift, TU Darmstadt, 2004.

Outside Mathematics:

  1. Kammermusik für Streichquartett und Gitarre, 2013. Score as a pdf; audio-files: 1. Satz, 2. Satz, 3. Satz, 4. Satz (all rights reserved; performances only with H. Glöckner's written consent)
Further information :