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Christian Bargetz – University of Innsbruck

Christian Bargetz

Christian Bargetz

Tel.: +43 512 507 53873
Fax: +43 512 507 53899
E-Mail: christian.bargetz [at] uibk.ac.at
Technikerstraße 13, 7.OG, Zi.-Nr.: 727
A-6020 Innsbruck

Current Teaching • Fields of Interest • Publications and Preprints • Conferences

Current Teaching

Office hours

By appointment (by email).

Courses in the Summer Term 2024

Suggested Topics for Bachelor theses

  • Extension operators for smooth and Lipschitz functions

Information on the organisation of the Bachelor seminar

Fields of Interest

  • Nonlinear functional analysis: Iterative methods in Hilbert and Banach spaces, Generic properties of nonexpansive mappings
  • Theory of locally convex spaces: Fréchet spaces, Sequence space representations, topological tensor products
  • Generalized Functions: vector-valued distributions

Publications

Preprints

  • C. Bargetz, M. Dymond, and K. Pirk, On extremal nonexpansive mappings. Preprint (arXiv:2409.04292)
  • C. Bargetz, J. Kąkol, and D. Sobota, Continuous operators from spaces of Lipschitz functions. Preprint (arXiv:2405.09930)

Journal Publications

  1. C. Bargetz, F. Luggin, and T. Russo, Tilings of the Hyperbolic Space and Lipschitz Functions. Canadian Journal of Mathematics. Published online 2024:1-21. DOI: 10.4153/S0008414X24000804, arXiv:2402.04201
  2. C. Bargetz, A. Bartoš, W. Kubiś, and F. Luggin, Homogeneous isosceles-free spaces. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 118 (2024). DOI: 10.1007/s13398-024-01587-y, arXiv:2305.03163
  3. C. Bargetz and F. Luggin, Observations on the metric projection in finite dimensional Banach spaces. Appl. Set-Valued Anal. Optim. 6 (2024), 41-52, DOI: 10.23952/asvao.6.2024.1.04, arXiv:2305.19908
  4. C. Bargetz, J. Kąkol, and D. Sobota, On complemented copies of the space \(c_0\) in spaces \(C_p(X,E)\), Math. Nachr. 297(2): 644-656. 2024. DOI: 10.1002/mana.202300026, arxiv:2107.03211
  5. C. Bargetz, S. Reich and D. Thimm: Generic properties of nonexpansive mappings on unbounded domains. J. Math. Anal. Appl. 526(1): Article 127179, 2023. DOI: 10.1016/j.jmaa.2023.127179, arXiv:2204.10279
  6. C. Bargetz, E. A. Nigsch and N. Ortner: Projective descriptions of spaces of functions and distributions. Math. Nachr. 296(3): 915-937, 2023 DOI: 10.1002/mana.202100526, arxiv:2109.14448
  7. C. Bargetz, E. Medjic, and K. Pirk: On generic convergence of successive approximations of mappings with convex and compact point images. Monatsh. Math. 202: 659–683, 2023. DOI: 10.1007/s00605-022-01813-y, arXiv:2211.02298
  8. C. Bargetz, A. Debrouwere, E. A. Nigsch: Sequence space representations for spaces of smooth functions and distributions via Wilson bases. Proc. Amer. Math. Soc. 150: 3841-3852, 2022, DOI: 10.1090/proc/15895, arxiv:2107.00245
  9. C. Bargetz, M. Dymond, E. Medjic and S. Reich: On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature. Topol. Methods Nonlinear Anal. 57(2): 621–634, 2021, DOI: 10.12775/TMNA.2020.040, arXiv:2004.02567
  10. C. Bargetz, E. A. Nigsch and N. Ortner: A simpler description of the \(\kappa\)-topologies on the spaces \(\mathscr{D}_{L^p}\), \(L^p\), \(\mathscr{M}^1\). Mathematische Nachrichten. 293(9): 1691–1706, 2020, DOI: 10.1002/mana.201900109,  arXiv:1711.06577
  11. C. Bargetz, J. Klemenc, S. Reich and  N. Skorokhod: On angles, projections and iterations. Linear Algebra Appl. 603 (2020): 41-56, DOI: 10.1016/j.laa.2020.05.023, arXiv:2004.07540
  12. C. Bargetz and E. Medjic: On the rate of convergence of iterated Bregman projections and of the alternating algorithm. J. Math. Anal. Appl. 481(1): Article 123482, 2020, DOI: 10.1016/j.jmaa.2019.123482, arXiv:1905.00605
  13. C. Bargetz and S. Reich: Generic Convergence of Sequences of Successive Approximations in Banach Spaces. Pure and Applied Functional Analysis 4(3): 477–493, 2019, arXiv:1903.10924, Link
  14. C. Bargetz, V. I. Kolobov, S. Reich, R. Zalas: Linear Convergence Rates for Extrapolated Fixed Point Algorithms. Optimization 68(1): 163–195, 2019, DOI: 10.1080/02331934.2018.1512109, arXiv:1805.03932
  15. C. Bargetz and N. Ortner: Kernel Identities and Vectorial Regularizations. Monatsh. Math. 186(2): 201–214, 2018, DOI: 10.1007/s00605-017-1076-4, arXiv:1509.07630
  16. C. Bargetz, S. Reich and R. Zalas: Convergence Properties of Dynamic String Averaging Projection Methods in the Presence of Perturbations. Numerical Algorithms 77(1): 185–209, 2018, DOI: 10.1007/s11075-017-0310-4, arXiv:1703.07803
  17. C. Bargetz and S.-A. Wegner: Pivot duality of universal interpolation and extrapolation spaces. Journal of Mathematical Analysis and Applications, 460(1): 321–331, 2018, DOI: 10.1016/j.jmaa.2017.11.042, arXiv:1604.00763
  18. C. Bargetz, M. Dymond und S. Reich: Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces. Topol. Methods Nonlinear Anal. 50(1):89–124, 2017, DOI: 10.12775/TMNA.2017.013, arXiv:1602.05230
  19. C. Bargetz, E. A. Nigsch, and N. Ortner: Convolvability and regularization of distributions. Annali di Matematica 196(6): 2239–2251, 2017, DOI: 10.1007/s10231-017-0662-3, arXiv:1505.04599
  20. C. Bargetz, J. Kąkol und W. Kubiś: A separable Fréchet space of almost universal disposition. J. Funct. Anal. 272(5): 1876–1891, 2017, DOI: 10.1016/j.jfa.2016.09.019, arXiv:1603.06361
  21. C. Bargetz and M. Dymond: σ-Porosity of the set of strict contractions in a space of non-expansive mappings. Israel J. Math. 214(1): 235–244, 2016, DOI: 10.1007/s11856-016-1372-z, arXiv:1505.07656
  22. C. Bargetz: Completing the Valdivia–Vogt tables of sequence-space representations of spaces of smooth functions and distributions. Monatsh. Math. 177(1): 1–14, 2015. DOI: 10.1007/s00605-014-0650-2
  23. C. Bargetz: Explicit representations of spaces of smooth functions and distributions. J. Math. Anal. Appl. 424: 1491–1505. 2015. DOI: 10.1016/j.jmaa.2014.12.009
  24. C. Bargetz and N. Ortner: Solution to the Cauchy problem for quasi-hyperbolic systems by vector-valued convolution. Appl. Anal. 94(11): 2355–2369, 2015. DOI: 10.1080/00036811.2014.985213
  25. C. Bargetz and N. Ortner: Characterization of L. Schwartz' convolutor and multiplier spaces \(\mathcal{O}_C'\) and \(\mathcal{O}_M\) by the short-time Fourier transform. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 108 (2): 833–847, 2014. DOI: 10.1007/s13398-013-0144-4
  26. C. Bargetz: Commutativity of the Valdivia–Vogt table of representations of function spaces. Mathematische Nachrichten 287(1): 10–22, 2014. DOI: 10.1002/mana.201200258
  27. C. Bargetz and N. Ortner: Convolution of vector-valued distributions: A survey and comparison. Dissertationes Mathematicae 495: 51 pp.,2013. DOI: 10.4064/dm495-0-1
  28. C. Bargetz: A sequence space representation of L. Schwartz' space \(\mathcal{O}_C\). Archiv der Mathematik 98(4): 317-326, 2012. DOI: 10.1007/s00013-012-0373-3
  29. C. Bargetz: Convolution of Distribution-Valued Functions. Applications. Revista Colombiana de Matemáticas 45(1): 51-80, 2011. Link

Theses

  • C. Bargetz: Topological Tensor Products and the Convolution of Vector-Valued Distributions. Dissertation. Universität Innsbruck. 2012. Advisor: ao.Univ.-Prof. Norbert Ortner
  • C. Bargetz: Impulsive Solutions of Differential Behaviors. Diplomarbeit. Universität Innsbruck, 2008. Advisor: o.Univ.-Prof. Ulrich Oberst

Projects

Past Projects

Conferences

Upcoming Conferences

Attended Conferences

2024 Banach spaces for analysts. A conference in honor of Professor Przemysław Wojtaszczyk. Będlewo, 14-19 July 2024
2023 Conference on Generic Structures, Bedlewo, 23-27 October 2023
  Bremen-Hamburg2-Kiel Seminar, Hamburg, 14 July 2023
  50th Winter School in Abstract Analysis, Sněžné, 7-14 January 2023
2022 International Conference on Generalized Functions, GF2022, 19-23 September 2022
  DMV Annual Meeting 2022, FU Berlin, 12-16 September 2022
  36th Summer Topology Conference, Vienna, July 18-22, 2022
2021 DMV-ÖMG Annual Conference 2021, University of Passau, 27 September–1 Oktober 2021

13th International ISAAC Congress, Ghent University@Zoom, 2–6 August 2021
2020 DMV Jahrestagung 2020, 14–17 September 2020
  48th Winter School in Abstract Analysis. Section Analysis. Svratka, 11–18 January 2020
2019 Analysis Seminar Innsbruck, 15th–17th November 2019

Workshop WDI2, Passau, 11th October 2019

ÖMG Conference 2019, Dornbirn, Austria, 16th–20th September 2019
  12th ISAAC Congress, University of Aveiro, Portugal, 29th July–2nd August 2019

Selected topics in stochastic geometry, Spring School, TU Darmstadt, 25 February–1 March 2019
  47th Winter School in Abstract Analysis. Section Analysis. Svratka, 12–19 January 2019
2018 CSASC 2018–Joint Meeting of the Czech, Slovenian, Austrian, Slovak and Catalan Mathematical Societies
Bratislava, Slovakia, September 11th–14th, 2018

International Conference on Generalized Functions GF2018, Novi Sad, Serbia, 27.–31. August, 2018 (link)

Workshop on Nonlinear Analysis and Optimization, The Technion, Haifa, 20 August 2018 (link)

Paweł Domański Memorial Conference, Będlewo, Poland, 1st–7th July 2018

Analysis Seminar, 2018, Traunkirchen, Austria, 8th–10th June 2018 (link)

Workshop: Wien – Innsbruck – Novi Sad, Innsbruck, 11–14 February 2018
  46th Winter School in Abstract Analysis. Section Analysis. Svratka, 13–20 January 2018
2017 Conference on Non Linear Functional Analysis, Valencia, 17–20 October 2017 (link)

19th ÖMG Congress and Annual DMV Meeting, Paris-Lodron University of Salzburg, 11-15 September 2017 (link)

7th German-Polish Conference on Optimization, 27 August 2017 - 1 September 2017, Będlewo (link)
  Septièmes journées Besançon-Neuchâtel d’analyse fonctionnelle. 20-23 juin 2017, Besançon (link) Lineare Algebra und Analytische Geometrie 2

Workshop on Nonlinear Analysis and Optimization, The Technion, Haifa, 7 February 2017 (link)

45th Winter School in Abstract Analysis. Section Analysis. Svratka, 14–21 January 2017
2016 Analysis Seminar Innsbruck 2016, 4–6 November 2016 (link)

44th Winter School in Abstract Analysis. Section Analysis. Svratka, 16–23 January 2016
2015 Relations Between Banach Space Theory and Geometric Measure Theory, Warwick, 8–12 June 2015 (link, slides)
  Workshop on Functional Analysis Valencia 2015 on the occasion of the 60th birthday of José Bonet,
Valencia, 15–19 June 2015 (link)
  49. Jahrestagung  der Gesellschaft für Didaktik der Mathematik, Basel, 9–13 February 2015 (poster)
  43rd Winter School in Abstract Analysis. Section Analysis. Svratka, 10–17 January 2015
2014
Analysis Seminar Innsbruck 2014, 24–26 October 2014 (link)
  Joint Meeting of the German Mathematical Society (DMV) and the Polish Mathematical Society (PTM), Poznań, 17–20 September 2014 (link)
  Young Functional Analysts' Meeting 2014, Debrecen, 11–13 April 2014VU/4 Nichtlineare Funktionalanalysis
  42nd Winter School in Abstract Analysis. Section Analysis. Svratka, 11–18 January 2014
2013 Analysis Seminar Innsbruck 2013, 29 November – 1 December 2013 (link)
  18th ÖMG Congress and Annual DMV Meeting University of Innsbruck, 23–27 September 2013 (link)
  Workshop on Functional Analysis Valencia 2013 on the occasion of the 60th birthday of Andreas Defant (link)
2012 37th Annual International Conference on Improving University Teaching Innsbruck, Austria 2012
  Functional Analysis: Applications to Complex Analysis and Partial Differential Equations 2012 organized in honor of Dietmar Vogt on the occasion of his 70th birthday (link)

Lecture Notes

(in German)

  • C. Bargetz and M. Dymond: Lipschitz Mappings and geometric properties of Banach Spaces. Summer term 2017
  • C. Bargetz: Lineare Algebra und Analytische Geometrie 2. Summer term 2017
  • C. Bargetz: Distributionentheorie und Anwendungen. Summer term 2012

Past Teaching

Summer term 2024 VO/3 Analysis 1, VO/1 Vertiefung Analysis, VO/4 Analysis 1
  VO/3 Analysis 4
  PS/2 Analysis 4
Winter term 2022/23 VO/3 Applied Mathematics
  PS/3 Applied Mathematics
Summer term 2022 SE/2 History and Philosophy of Mathematics (with W. Löffler)
  PS/2 Analysis 2
Winter term 2021/22  
Summer term 2021 VU/4 Topology meets Geometry: Dimension, Fractals and Metric Geometry (with U. Grupel)
  SE/2 History and Philosophy of Mathematics (with W. Löffler)
Winter term 2020/21 VU/4 Subject-Specific Fundamentals and Core Skills 1: Geometry, Measure and Banach Spaces (with U. Grupel)
OLAT course
  SE/2 History and Philosophy of Mathematics (with W. Löffler)
OLAT course
Summer term 2020 VO/4 Linear Algebra and Analytic Geometry 2
  SE/2 History and Philosophy of Mathematics (with W. Löffler)
Winter term 2019/20 VU/4 Nonlinear Functional Analysis
OLAT-Kurs
Summer term 2019 PS/2 Analysis 2
OLAT course
  VU/2 Analysis und Stochastik im Schulunterricht
OLAT course
Winter term 2018/19 VU/2 Analysis und Stochastics at School
OLAT course
Summer term 2018 VO/4 Linear Algebra and Analytic Geometry 2
OLAT course
  PS/2 Linear Algebra and Analytic Geometry 2
OLAT course
Winter term 2017/18 VU/4 Functional Analysis
OLAT course
  SE/2 Research Seminar: Functional Analysis - Current Research WS 2017/18
OLAT course • Seminar Website
Summer term 2017 VO/4 Linear Algebra and Geometry 2
OLAT course • First problem sheet • OLAT course for the exercises

VU/4 Lipschitz mappings and geometric properties of Banach spaces
OLAT course
Winter term 2016/17 PS/2 Linear Algebra 1 for Physicists
Summer term 2015 VO/4 Linear Algebra and Geometry 2
  SE/2 Seminar
Winter term 2014/15 SL/1 Linear Algebra and Geometry 1
  PS/1 Linear Algebra and Geometry 1
Summer term 2014 VO/4 Linear Algebra and Geometry 2
  PS/2 Linear Algebra and Geometry 2
Winter term 2013/14 SL/1 Linear Algebra and Geometry 1
  PS/1 Linear Algebra and Geometry 1
Summer term 2013 SL/1 Analysis 1
  PS/1 Analysis 2
  PS/2 Analysis 2
  SE/2 Seminar with Bachelor thesis
Winter term 2012/13 PS/2 Analysis 1
Summer term 2012 VO/2 Distribution Theory and Applications
Winter term 2011/12 PS/2 Analysis 3
Summer term 2011 PS/2 Analysis 2
Winter term 2010/11 PR/1 Introduction to Mathematics 2
  PS/2 Optimisation
Wintersemester 2009/10 PS/2 Introduction to Mathematics 2
  PR/1 Introduction to Mathematics 2
  UE/4 Programming Language 1, Tutorial
Wintersemester 2008/09 PR/1 Introduction to Mathematics 2
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