Professor, University of Leipzig

Postal address	Institute of Mathematics, University of Leipzig P.O. Box 100 920, 04009 Leipzig, Germany
Visiting address	Office A 427, Augustusplatz 10, 04109 Leipzig (map)
Phone (Fax)	+49 341 97 32167   (+49 341 97 32187)
E-Mail	eisner @ math.uni-leipzig.de

Internet Seminar "Ergodic Structure Theory and Applications"
Perspectives on Ergodic Theory and its Interactions
Summer School on Additive Combinatorics, Number Theory and Ergodic Theory

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Research Interests - Curriculum Vitae - Books - Papers - Teaching - Links

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Main Research Interests

• functional analysis/ operator theory
• dynamical systems/ ergodic theory
  

Curriculum Vitae

pdf-file

Books

Tanja Eisner, Bálint Farkas A Journey Through Ergodic Theorems Birkhäuser Advanced Texts Basler Lehrbücher, Birkhäuser Verlag, to appear. (For a draft version please write us an email.) Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel Operator Theoretic Aspects of Ergodic Theory Graduate Texts in Mathematics, Springer, 2015. 628 pp. (Here you can find a draft version.) Tanja Eisner Stability of Operators and Operator Semigroups Operator Theory: Advances and Applications, Vol. 209. Birkhäuser Verlag, Basel, 2010. 204 pp. (Here you can find a draft version.) Tanja Eisner, Birgit Jacob, André Ran, Hans Zwart (eds.) Operator Theory, Function Spaces, and Applications, International Workshop on Operator Theory and Applications, Amsterdam, July 2014. Operator Theory: Advances and Applications, Birkhäuser Verlag, 2016.

Papers

35. A view on multiple recurrence, Indag. Math. 34 (2023), 231-247. (Special issue on the occasion of Jaap Korevaar's 100-th birthday) [arXiv]
    
36. (with Agnes Radl) Embeddability of real and positive operators, Linear Multilinear Algebra 70 (2022), 3747-3767. [arXiv]
    
37. (with Zoltán Buczolich) Divergence of weighted square averages in L¹, Adv. Math. 384 (2021), Paper No. 107727, 19 pp. [arXiv]
    
38. (with Vladimir Müller) Power bounded operators and the mean ergodic theorem for subsequences, J. Math. Anal. Appl. 493 (2021), 124523, 25 pp. [arXiv]
    
39. Nilsystems and ergodic averages along primes, Ergodic Theory Dynam. Systems 40 (2020), 2769-2777. [arXiv]
    
40. (with Guy Cohen, Christophe Cuny and Michael Lin) Resolvent conditions and growth of powers of operators, J. Math. Anal. Appl. 487 (2020), 124035, 24 pp. [arXiv]
    
41. (with Bálint Farkas and Christophe Cuny) Wiener's lemma along primes and other subsequences, Adv. Math. 347 (2019), 340-383. [arXiv]
    
42. (with Jakub Konieczny) Automatic sequences as good weights for ergodic theorems, Discrete Contin. Dyn. Syst. 38 (2018), no. 8, 4087-4115. [arXiv]
    
43. (with Michael Lin) On modulated ergodic theorems, J. Nonlinear Var. Anal. 2 (2018), 131-154. (special issue dedicated to Simeon Reich). [arXiv]
    
44. (with Dávid Kunszenti-Kovács) On the pointwise entangled ergodic theorem, J. Math. Anal. Appl. 449 (2017), 1754-1769. [arXiv]
    
45. (with Ben Krause) (Uniform) convergence of twisted ergodic averages, Ergodic Theory Dynam. Systems 36 (2016), 2172-2202. [arXiv]
    
46. A polynomial version of Sarnak's conjecture, C. R. Math. Acad. Sci. Paris 353 (2015), 569-572. [arXiv]
    
47. Linear sequences and weighted ergodic theorems, Abstr. Appl. Anal. 2013, Art. ID 815726. [arXiv]
    
48. (with Tamás Mátrai) On typical properties of Hilbert space operators, Israel J. Math. 195 (2013), 247-281. [arXiv]
    
49. (with Pavel Zorin-Kranich) Uniformity in the Wiener-Wintner theorem for nilsequences, Discrete Contin. Dyn. Syst. 33 (2013) 3497-3516. [arXiv]
50. (with Dávid Kunszenti-Kovács) On the entangled ergodic theorem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. XII (2013), 141-156. [arXiv]
    
51. (with Terence Tao) Large values of the Gowers-Host-Kra seminorms, J. Anal. Math. 117 (2012), 133-186. [arXiv]
52. (with Sophie Grivaux) Hilbertian Jamison sequences and rigid dynamical systems, J. Funct. Anal. 261 (2011), 2013-2052. [arXiv]
53. (with Tim Austin and Terence Tao) Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems, Pacific J. Math. 250 (2011), 1-60. [arXiv]
54. A "typical" contraction is unitary, Enseign. Math. (2) 56 (2010), 403-410. [arXiv]
55. (with András Serény) On the weak analogue of the Trotter-Kato theorem, Taiwanese J. Math. 14 (2010), 1411-1416. [arXiv]
56. Embedding operators into strongly continuous semigroups, Arch. Math. (Basel) 92 (2009), 451-460. [arXiv]
    
57. (with András Serény) Category theorems for stable semigroups, Ergodic Theory Dynamical Systems 29 (2009), 487-494. [arXiv]
58. (with Hans Zwart) The growth of a C₀-semigroup characterised by its cogenerator, J. Evol. Equ. 8 (2008), 749-764. [arXiv]
59. (with András Serény) Category theorems for stable operators on Hilbert spaces, Acta Sci. Math. (Szeged) 74 (2008), 259-270. [arXiv]
60. (with András Bátkai and Yuri Latushkin) The spectral mapping property of delay semigroups, Compl. Anal. Oper. Theory 2 (2008), 273-283. [pdf-file]
61. (with Hans Zwart) A note on polynomially growing C₀-semigroups, Semigroup Forum 75 (2007), 438-445. [pdf-file]
62. (with Bálint Farkas, Rainer Nagel and András Serény) Weakly and almost weakly stable C₀-semigroups, Int. J. Dyn. Syst. Differ. Equ. 1 (2007), 44-57. [arXiv]
63. (with Hans Zwart) Continuous-time Kreiss resolvent condition on infinite-dimensional spaces, Math. Comp. 75 (2006), 1971-1985. [pdf-file]
    
64. Polynomially bounded semigroups, Semigroup Forum 70 (2005), 118-126. [pdf-file], [erratum]
65. (with Olga M. Katkova and Anna M. Vishnyakova) On entire functions having Taylor sections with only real zeros, Mat. Fiz. Anal. Geom. 11 (2004), 449-469.
66. (with Olga M. Katkova and Anna M. Vishnyakova) On power series having sections with only real zeros, Comput. Methods Funct. Theory 3 (2003), 425-441.
67. On variation preserving operators, Mat. Fiz. Anal. Geom. 10 (2003), 94-105.
    

Papers in proceedings

2. (with Rainer Nagel) Arithmetic progressions - an operator theoretic view, Discrete Contin. Dyn. Syst. Series S, 6 (2013), 657-667.
   
3. (with Bálint Farkas) Weak stability of orbits of C₀-semigroups on Banach spaces. In H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Below (eds), Functional Analysis and Evolution Equations. The Günter Lumer Volume (2007), 201-208. [pdf-file]
   

Miscellaneous

• Rigidity of contractions on Hilbert spaces. [arXiv]
  

Some Teaching

• Topology (Summer 2018)
• Analysis I (Winter 2018/19)
• Analysis II (Summer 2019)
• Ergodic Theory (Summer 2019)
• Ergodic Theory II (Summer 2017)
• Functional Analysis II (Summer 2018)
• Seminar "Operator Theory" (Winter 2018/19)
• Internet Seminar "Ergodic Theorems" (2018/2019)

Links

Study/career advice from Anton Deitmar and Terence Tao
n-City-Seminar     "Dynamics and Geometry" Seminar     Functional Analysis Group
Journal for Analysis and Its Applications     Max Planck Institute for Math. in the Sciences
Miniworkshops on Operator Theoretic Aspects of Ergodic Theory ( Leipzig, Kiel, Wuppertal, Tübingen, Feldkirch, Leipzig, Wuppertal, Kiel)
MathSciNet     ArXiv     Trains in Germany     Functional analysis group Tübingen     Colloquium in Honour of Thomas Kühn