Publications of Jürgen Grahl


  1. Using oscillating functions to disprove misconceptions on real-valued functions
    (with Shahar Nevo)
    to appear in Mathematics Magazine

  2. On the growth of real functions and their derivatives
    (with Shahar Nevo)
    Real Anal. Exch. 43 (2018), 333-346

  3. Differential inequalities and a Marty-type criterion for quasi-normality
    (with Tomer Manket and Shahar Nevo)
    J. Austr. Math. Soc. 105 (2018), 34-45

  4. Quasi-normality induced by differential inequalities
    (with Shahar Nevo)
    Bull. Lond. Math. Soc. 50 (2018), 73-84

  5. Differential inequalities and quasi-normal families
    (with Roi Bar and Shahar Nevo)
    Anal. Math. Phys. 4 (2014), 63-71

  6. Exceptional functions wandering on the sphere and normal families
    (with Shahar Nevo)
    Isr. J. Math. 202 (2014), 21-34

  7. An extension of one direction in Marty's normality criterion
    (with Shahar Nevo)
    Monatsh. Math. 174 (2014), 205-217

  8. On Riemann's theorem about conditionally convergent series
    (with Shahar Nevo)
    N. Z. J. Math. 43 (2014), 85-93

  9. A non-explicit counterexample to a problem of quasi-normality
    (with Shahar Nevo and Xuecheng Pang)
    J. Math. Anal. Appl. 406 (2013), 386-391

  10. On a result of Bergweiler and Eremenko concerning derivatives bounded on preimages of unbounded sets
    Comput. Methods Funct. Theory 13 (2013), 181-187

  11. Spherical derivatives and normal families
    (with Shahar Nevo)
    J. d'Anal. Math. 117 (2012), 119-128

  12. A normality criterion involving rotations and dilations in the argument
    Arkiv Math. 50 (2012), 89-110

  13. Differential polynomials and shared values
    (with Shahar Nevo)
    Ann. Acad. Sci. Fenn. Math. 36 (2011), 47-70

  14. Differential polynomials with dilations in the argument and normal families,
    Monatsh. Math. 162 (2011), 429-452

  15. Uniqueness theorems for L-functions
    (with Ramunas Garunkštis and Jörn Steuding)
    Comment. Math. Univ. St. Pauli 60 (2011), 15-35

  16. Differential polynomials which share a value with their derivative and normal families
    Analysis 31 (2011), 67-80

  17. On a result of Singh and Singh concerning shared values and normality
    (with Shahar Nevo),
    Compl. Var. Elliptic Equ. 55 (2010), 347-356

  18. A modification of the Nevanlinna theory
    Comput. Methods Funct. Theory10 (2010), 97-109.

  19. An extension of Lewis's lemma, renormalization of harmonic and analytic functions and normal families
    (with Oliver Roth)
    Math. Nachr. 282 (2009), 540-551

  20. Some new results on the semiduality of small sets of analytic functions,
    Analysis 29 (2009), 71-80

  21. Entire functions sharing a polynomial with their derivatives and normal families
    (with Chao Meng)
    Analysis 28 (2008), 51-61

  22. An addition to the Tumura-Clunie theorem
    Result. Math. 52 (2008), 55-61

  23. A short proof of Miranda's theorem and some extensions using Zalcman's lemma,
    J. Anal. 11 (2003), 105-113

  24. On the construction of semidual gap structures,
    Analysis 23 (2003), 185-198

  25. Hayman's alternative and normal families of nonvanishing meromorphic functions
    Comput. Methods Funct. Theory 2 (2002), 481-508.

  26. Semiduality of small sets of analytic functions
    Comput. Methods Funct. Theory 2 (2002), 113-135.

  27. An extension of a normality result of D. Drasin and H. Chen & X. Hua for analytic functions
    Comput. Methods Funct. Theory1 (2001), 457-478.

  28. Some applications of Cartan's theorem to normality and semiduality of gap power series,
    J. d'Anal. Math. 82 (2000), 207-220

Economy and Ecology

  1. Zehn fragwürdige Dogmen und Paradigmen der traditionellen Ökonomie (Ten disputable dogmata and paradigms of standard economy)
    Jahrbuch Nachhaltige Ökonomie 2013/2014, ed.: H. Rogall et al., Metropolis, Marburg 2013, 135-154

  2. Das Loch im Fass - Energiesklaven, Arbeitsplätze und die Milderung des Wachstumszwangs (The hole in the bucket - energy slaves, jobs and the mitigation of the need to grow)
    (with Reiner Kümmel),
    Nachhaltiges Wachstum: Wissenschaft und Umwelt Interdisziplinär 13 (2009), 195-212

  3. Von Wachstum und Wachstumszwang (About growth and the force to grow)
    (with Stefan Brunnhuber)
    GAIA 16/3 (2007), 176-177

  4. Jenseits des Wachstumszwangs. Zum Verhältnis von Energie, Kapital und Arbeit (Beyond the need to grow)
    (with Stefan Brunnhuber)
    GAIA 15/2 (2006), 96-101


  1. Estimates for probabilities of independent events and infinite series
    (with Shahar Nevo)