Helge Glöck­ner's Pub­lic­a­tions and Pre­prints

Total number of publications (excluding preprints and theses): 88

Articles in refereed mathematical journals:

  1. Diffeomorphism groups of real analytic manifolds are L^1-regular, to appear in Nonlinear Analysis (cf.arXiv:2007.15611)
  2. Deep neural networks on diffeomorphism groups for optimal shape reparameterization (with E. Celledoni, J. Riseth, and A. Schmeding), BIT 63 (2023), no. 4, paper no. 50, 38 pp.
  3. 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.
  4. Diffeomorphism groups of convex polytopes, J. Convex Anal. 30 (2023), 343-358.
  5. Aspects of control theory on infinite-dimensional Lie groups and G-manifolds (with J. Hilgert), J. Differ. Equations 343 (2023), 186-232.
  6. Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces, Axioms 11 (2022), no. 5, article 221 (open access)
  7. Non-Lie subgroups in Lie groups over local fields of positive characteristic, p-Adic Numbers Ultrametric Anal. Appl. 14 (2022), no. 2, 138-144.
  8. Manifolds of mappings on Cartesian products (with A. Schmeding), Ann. Global Anal. Geom. 61 (2022), 359-398.
  9. Locally pro-p contraction groups are nilpotent (with G.A. Willis), J. Reine Angew. Math. 781 (2021), 85-103.
  10. Decompositions of locally compact contraction groups, series and extensions (with G.A. Willis), J. Algebra 570 (2021), 164-214.
  11. Direct limits of regular Lie groups, Math. Nachr. 294 (2021), no. 1, 74-81.
  12. Lie groupoids of mappings taking values in a Lie groupoid (with H. Amiri and A. Schmeding), Arxivum Math. 56 (2020), no. 5, 307-356.
  13. Products of regular locally compact spaces are kR-spaces (with N. Masbough), Top. Proc. 55 (2020), 35-38.
  14. Completeness of infinite-dimensional Lie groups in their left uniformity, Canadian J. Math. 71 (2019), no. 1, 131-152.
  15. 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.
  16. Completeness of locally komega-groups and related infinite-dimensional Lie groups, Topol. Appl. 228 (2017), 277-284.
  17. Diffeomorphism groups of compact convex sets (with Karl-Hermann Neeb), Indag. Math. 28 (2017), 760--783.
  18. Elementary p-adic Lie groups have finite construction rank, Proc. Amer. Math. Soc. 145 (2017), no. 11, 5007-5021.
  19. Expansive automorphisms of totally disconnected, locally compact groups (with C.R.E. Raja), J. Group Theory 20 (2017), no. 3, 589-619.
  20. Homotopy groups of ascending unions of infinite-dimensional manifolds, to appear in Ann. Inst. Fourier (Grenoble) (cf. arXiv:0812.4713v2)
  21. 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.
  22. Bounded solutions of finite lifetime to differential equations in Banach spaces (with R. Dahmen), Acta Sci. Math. (Szeged) 81 (2015), 457-468.
  23. Weighted inversion of general Dirichlet series (with L.G. Lucht), Trans. Amer. Math. Soc. 366 (2014), no. 6, 3275-3293.
  24. Continuity of convolution of test functions on Lie groups (with L. Birth), Canadian J. Math. 66 (2014), no. 1, 102-140.
  25. Exponential laws for ultrametric partially differentiable functions and applications, p-Adic Numbers Ultram. Anal. Appl. 5 (2013), no. 2, 122-159.
  26. Continuity of LF-algebra representations associated to representations of Lie groups, Kyoto J. Math. 53 (2013), no. 3, 567-595.
  27. Invariant manifolds for analytic dynamical systems over ultrametric fields, Expo. Math. 31 (2013), 116-150.
  28. When unit groups of continuous inverse algebras are regular Lie groups (with K.-H. Neeb), Studia Math. 211 (2012), 95-109.
  29. Upper bounds for continuous seminorms and special properties of bilinear maps, Topol. Appl. 159 (2012), 2990-3001.
  30. Continuity of bilinear maps on direct sums of topological vector spaces, J. Funct. Anal. 262 (2012), no. 5, 2013-2030.
  31. Topological algebras of rapidly decreasing matrices and generalizations (with B. Langkamp), Topol. Appl. 159 (2012), 2420-2422.
  32. 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.
  33. Final group topologies, Kac-Moody groups and Pontryagin duality (with R. Gramlich and T. Hartnick), Israel J. Math. 177 (2010), 49-102.
  34. General Dirichlet series, arithmetic convolution equations and Laplace transforms (with L.G. Lucht and S. Porubsky), Stud. Math. 193 (2009), no. 2, 109-129.
  35. Solutions to open problems in Neeb's recent survey on infinite-dimensional Lie groups, Geom. Dedicata 135 (2008), 71-86.
  36. Contractible Lie groups over local fields, Math. Z. 260 (2008), 889-904
  37. Ultrametric and non-locally convex analogues of the general curve lemma of convenient differential calculus, Glasgow Math. J. 50 (2008), no. 2, 271-288.
  38. Comparison of some notions of C^k-maps in multi-variable non-archimedian analysis, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 877-904.
  39. Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories, J. Funct. Anal. 245 (2007), 19-61.
  40. Direct limit groups do not have small subgroups, Topol. Appl. 154 (2007), 1126-1133.
  41. Solutions to arithmetic convolution equations (with L.G. Lucht and S. Porubsky), Proc. Amer. Math. Soc. 135 (2007), 1619-1629.
  42. 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.
  43. Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces, J. Math. Kyoto Univ. 47 (2007), 631-642.
  44. Simplified Proofs for the Pro-Lie Group Theorem and the One-Parameter Subgroup Lifting Lemma, J. Lie Theory 17 (2007), 899-902.
  45. Implicit functions from topological vector spaces to Banach spaces, Israel J. Math. 155 (2006), 205-252.
  46. Every smooth p-adic Lie group admits a compatible analytic structure, Forum Math. 18 (2006), 45-84.
  47. 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.
  48. Fundamental problems in the theory of infinite-dimensional Lie groups, J. Geom. Symm. Phys. 5 (2006), 24-35.
  49. Discontinuous non-linear mappings on locally convex direct limits, Publ. Math. Debrecen 68/1-2 (2006), 1-13
  50. Hölder continuous homomorphisms between infinite-dimensional Lie groups are smooth, J. Funct. Analysis 228 (2005), no. 2, 419-444.
  51. Conveniently Hölder homomorphisms are smooth in the convenient sense, Ann. Global Anal. Geom. 27 (2005), 227-255.
  52. Fundamentals of direct limit Lie theory, Compositio Math. 141 (2005), 1551-1577.
  53. Smooth Lie groups over local fields of positive characteristic need not be analytic, J. Algebra 285 (2005), 356-371.
  54. Diff(R^n) as a Milnor-Lie group, Math. Nachr. 278 (2005), No. 9, 1025-1032.
  55. Contraction groups for tidy automorphisms of totally disconnected groups, Glasgow Math. J. 47 (2005), no. 2, 329-333.
  56. Differential calculus over general base fields and rings (with W. Bertram and K.-H. Neeb), Expo. Math. 22 (2004), 213-282.
  57. Tensor products in the category of topological vector spaces are not associative, Comment. Math. Univ. Carol. 45 (2004), no. 4, 607-614.
  58. Examples of differentiable mappings into non-locally convex spaces, Topol. Proc. 28 (2004), No. 2, 479-486.
  59. Positive definite functions on infinite-dimensional convex cones, Memoirs Amer. Math. Soc. 789 (2003), xiv+128 pp
  60. Banach-Lie quotients, enlargibility, and universal complexifications (with K.-H. Neeb), J. Reine Ang. Math. 560 (2003), 1-28.
  61. Direct limit Lie groups and manifolds, J. Math. Kyoto Univ. 43 (2003), 1- 26.
  62. Lie groups of measurable mappings, Canadian J. Math. 55 (2003), no. 5, 969-999.
  63. Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups, J. Funct. Analysis 194 (2002), No. 2, 347-409.
  64. Algebras whose groups of units are Lie groups, Studia Math. 153 (2002), 147-177.
  65. Topologization of Hecke pairs and Hecke C*-algebras (with G.A. Willis), Topol. Proc. 26 (2001-2002), No. 2, 565-591.
  66. Approximation by p-adic Lie groups, Glasgow Math. J. 44 (2002), 231-239.
  67. Real and p-adic Lie algebra functors on the category of topological groups, Pacific J. Math. 203 (2002), No. 2, 321-368.
  68. Uniscalar p-adic Lie groups (with G. A. Willis), Forum Math. 13 (2001), 413-421.
  69. Functions operating on positive semidefinite quaternionic matrices, Monatsh. Math. 132 (2001), No.4, 303-324.
  70. Representations of cones and conelike semigroups, Semigroup Forum 60 (2000), 326-333.
  71. Scale functions on p-adic Lie groups, Manuscr. Math. 97 (1998), 205-215.
  72. Scale functions on linear groups over local skew fields, J. Algebra 205 (1998), 525-541.
  73. 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. L^1-regularity of strong ILB-Lie groups (with A. Suri), preprint, 17 pp, October 2024; arXiv:2410.02909
  2. Boundary values of diffeomorphisms of simple polytopes, and controllability (with E. Grong and A. Schmeding), preprint, 34 pp, July 2024; arXiv:2407.05444
  3. Manifolds of continuous BV-functions and vector measure regularity of Banach-Lie groups (with A. Schmeding and A. Suri), preprint, 55 pp, July 2024; arXiv:2407.05190
  4. Birkhoff decompositions for loop groups with coefficient algebras, preprint, 28 pp, June 2022; arXiv:2206.11711
  5. Contraction groups and the big cell for endomorphisms of Lie groups over local fields, preprint, 34 pp, January 2021; arXiv:2101.02981
  6. Smoothing operators for vector-valued functions and extension operators, preprint, 118 pp, May 2020; arXiv:2006.00254
  7. Measurable regularity properties of infinite-dimensional Lie groups, preprint, 229 pp, December 2015; arXiv:1601.02568
  8. Fundamentals of submersions and immersions between infinite-dimensional manifolds, preprint, 39 pp, October 2016 (first version: February 2015); arXiv:1502.05795
  9. 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
  10. Regularity properties of infinite-dimensional Lie groups and semiregularity, preprint, 68 pp, February 2016 (first version: August 2012), arXiv:1208.0715
  11. 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
  12. Implicit functions from topological vector spaces to Frechet spaces in the presence of metric estimates, preprint, 51 pp, December 2006; math/0612673
  13. Lie groups over non-discrete topological fields, preprint, 128 pp, August 2004; math/0408008
  14. Patched locally convex spaces, almost local mappings, and diffeomorphism groups of non-compact manifolds, manuscript.
  15. 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: