R. Michael Range

Ph. D. 1971, University of California, Los Angeles; Diplom 1968, University of Göttingen, Germany




Multidimensional complex analysis, integral representations, boundary regularity of the Cauchy-Riemann equations, spaces of holomorphic functions in several variables, function algebras



Calculus Curriculum, Historical Aspects of Multidimensional Complex Analysis


  • Short Course "Integral Kernel Methods for Weakly Pseudoconvex Domains". Chinese Academy of Sciences, Beijing, April 2014
  • Colloquium Lecture, University of Arkansas, Nov. 2012
  • Special Lecture at Math Club, Univ. of Arkansas, Nov. 2012
  • Special Session "Complex Analysis and its Broader Impact" at the AMS Regional Meeting in Akron, Ohio, October 2012
  • Lecture at University of Tokyo, Japan, July 2012
  • Lecture at Hayama International Symp. on Sev. Complex Variables, Shonan Center, Japan, July 2012
  • Colloquium Lecture, Xiamen University, China, October 2011
  • Special Lecture on Calculus, Jiaxing University, China, October 2011
  • Colloquium Lecture, Chinese Academy of Sciences, Beijing, October 2011
  • Special Lecture on Calculus, Chinese Academy of Sciences, Beijing, October 2011
  • Seminar Lecture, Lebanese American University, Beirut, May 2011
  • Seminar Lecture, University of California at Los Angeles, March 2011
  • Colloquium Lecture, University of Utah, Salt Lake City, March 2011
  • Undergraduate Colloquium, University of Utah, Salt Lake City, February 2011
  • Workshop on the d-bar Neumann Problem, E. Schroedinger International Inst., Vienna, November 2009
  • Colloquium Lecture, University of Ghana, Legon (Accra), April 2007
  • Oka Centennial Conference, Kyoto, Japan, October 2001
  • Special Session on Complex Analysis, Joint Meeting AMS and SMM, Morelia, Mexico, May 2001
  • Frontiers in Mathematics Lecturer, 3 lectures, Texas A&M University, April 2001
  • Seminar Lecture, Univ. of Bologna, Italy, June 2000
  • Special Session on Several Complex Variables, AMS Annual Meeting, San Antonio, 1999
  • Mathematical Sciences Research Institute (MSRI), Berkeley, 1996
  • International Conference "Operator Theory for Complex and Hypercomplex Analysis", Mexico City, 1994
  • Colloquium Lecture, University of Notre Dame, 1994
  • Colloquium Lecture, University of Maryland, 1992
  • International Conference "Complex Analysis and Geometry", Trento, Italy, 1991
  • Seminar Lecture, Harvard University, 1990
  • Seminar Lecture, Princeton University, 1989
  • International Conference "Geometry and Complex Variables in Bologna", in celebration of the 9th centenary of the University of Bologna, Italy, 1989



    What is Calculus? From Simple Algebra to Deep Analysis. Manuscript xiv + 259 pp. (2012) (Under Review)

    Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, New York 1986. 2nd corrected printing 1998.


    1. Descartes's Double Point Method for Tangents: An Old Idea Suggests New Approaches to Calculus. Notices Amer. Math. Soc. 61(4) (2014), 387-389.
    2. A Pointwise a-priori Estimate for the d-bar Neumann Problem on Weakly Pseudoconvex Domains. arXiv:1106.3132 (2013).
    3. A New Integral Kernel for Weakly Pseudoconvex Domains. Math. Ann. 356(2013), 793-808.
    4. What is....a Pseudoconvex Domain? Notices Amer. Math. Soc. 59 (2012), 301-303.
    5. Where are Limits Needed in Calculus? Amer. Math. Monthly 118 (2011), 404-417.
    6. Some landmarks in the history of the tangential Cauchy-Riemann equations. Rendiconti di Matematica, Serie VII, 30 (2010) , 275-283.
    7. On Antiderivatives of the Zero Function. Mathematics Magazine 80 (2007), 387 - 390
    8. Kneser's paper on the boundary values of analytic functions of two variables. In: Hellmuth Kneser, Gesammelte Abhandlungen, 872 - 876, ed. G. Betsch and K. H. Hofman, deGruyter, Berlin 2005
    9. On the Decomposition of Holomorphic Functions by Integrals and the Local CR Extension Theorem. Adv. Studies in Pure Math. 42 (2004), Math. Soc. Japan, 269 - 273.
    10. Complex Analysis: A Brief Tour into Higher Dimensions, Amer. Math. Monthly 110 (2003), 89 - 108.
    11. (Selected for the 2004 Lester R. Ford Award of the Mathematical Association of America.)
    12. Extension Phenomena in Multidimensional Complex Analysis: Correction of the Historical Record. The Mathematical Intelligencer 24, no 2 (2002), 4 - 12
    13. On d-bar Problems on (Pseudo) - Convex Domains. Topics in Complex Analysis, Banach Center Publ. 31, 311 - 320, Polish Acad. of Sci., Warszawa 1995
    14. Integral Kernels and Hölder Estimates for d-bar on pseudoconvex domains of finite type in C^2. Math. Ann. 288 (1990), 63 - 74
    15. Cauchy-Fantappie Formulas in Multidimensional Complex Analysis. Proc. Int. Conf. "Geometry and Complex Analysis", Bologna 1989, Lect. Notes in Pure and Appl. Math 132, 307 - 32, Marcel Dekker, New York 1991
    16. Integral Representations and Estimates in the Theory of the d-bar Neumann Problem. (with I. Lieb) Ann. of Math. 123 (1986), 265 - 301