# Helge Glöckner's Publications and Preprints

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

### Articles in refereed mathematical journals:

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

### Articles in refereed conference proceedings:

*Endomorphisms of Lie groups over local fields*, pp. 101-165 in: "2016 MATRIX Annals," Springer-Verlag, Cham, 2018.*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.*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.*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.*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.*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.*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.*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.*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.*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:

*Regularity properties of infinite-dimensional Lie groups*, Oberwolfach Rep.**13**(2013), 791-794.*Homotopy groups of topological spaces containing a dense directed union of manifolds*, Oberwolfach Rep.**7**(2010), no. 4, 3037-3039*Direct limits of infinite-dimensional Lie groups*, Oberwolfach Rep.**3**(2006), no. 4, 3286-3289*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.*Direct limits of Lie groups*, Oberwolfach Rep.**1**(2004), no. 1, 321-324.

### Books edited

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

### Preprints and submitted articles:

*Birkhoff decompositions for loop groups with coefficient algebras*, preprint, 28 pp, June 2022; arXiv:2206.11711*Contraction groups and the big cell for endomorphisms of Lie groups over local fields,*preprint, 34 pp, January 2021; arXiv:2101.02981*Diffeomorphism groups of real analytic manifolds are L^1-regular,*preprint, 47 pp, September 2023 (first version July 2020); arXiv:2007.15611*Smoothing operators for vector-valued functions and extension operators*, preprint, 118 pp, May 2020; arXiv:2006.00254*Measurable regularity properties of infinite-dimensional Lie groups*, preprint, 229 pp, December 2015; arXiv:1601.02568*Fundamentals of submersions and immersions between infinite-dimensional manifolds*, preprint, 39 pp, October 2016 (first version: February 2015); arXiv:1502.05795*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*Regularity properties of infinite-dimensional Lie groups and semiregularity*, preprint, 68 pp, February 2016 (first version: August 2012), arXiv:1208.0715*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*Implicit functions from topological vector spaces to Frechet spaces in the presence of metric estimates*, preprint, 51 pp, December 2006; math/0612673*Lie groups over non-discrete topological fields*, preprint, 128 pp, August 2004; math/0408008*Patched locally convex spaces, almost local mappings, and diffeomorphism groups of non-compact manifolds*, manuscript.*Differentiable mappings between spaces of sections*, manuscript, 2002, 30 pp. (now a preprint: arXiv:1308.1172)

### Theses:

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