R. Michael Range

Ph. D. 1971, University of California, Los Angeles; Diplom 1968, University of G�ttingen, Germany

ACADEMIC POSITIONS:

RESEARCH POSITIONS:

RESEARCH INTERESTS

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

AWARDS and RECOGNITIONS

OTHER ACADEMIC INTERESTS

Calculus Curriculum, Historical Aspects of Multidimensional Complex Analysis

RECENT INVITED LECTURES (partial list)

Ph.D. STUDENTS

PUBLICATIONS

BOOKS:

What is Calculus? From Simple Algebra to Deep Analysis. xxxii + 340 pp., World Scientific Publishing, Singapore, 2015.

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

SELECTED RECENT ARTICLES:

  1. Integral Representations in Complex Analysis: From Classical Results to Recent Developments. In: Advancements in Complex Analysis, Daniel Breaz and Michael Th. Rassias, Editors, pp. 449 - 471, Springer Nature Switzerland 2020
  2. Using high school algebra for a natural approach to derivatives and continuity. The Mathematical Gazette (London) 102 (2018), 435 - 446.
  3. A Pointwise a-priori Estimate for the d-bar Neumann Problem on Weakly Pseudoconvex Domains. Pacific J. Math. 275 (2015), 409 - 432.
  4. Descartes's Double Point Method for Tangents: An Old Idea Suggests New Approaches to Calculus. Notices Amer. Math. Soc. 61(4) (2014), 387-389. Edited and Translated: Von Descartes zu einem neuen Zugang zur Differentialrechnung und Analysis. Mitteilungen der DMV (2016), 26 -29.
  5. A New Integral Kernel for Weakly Pseudoconvex Domains. Math. Ann. 356(2013), 793-808.
  6. What is....a Pseudoconvex Domain? Notices Amer. Math. Soc. 59 (2012), 301-303.
  7. Where are Limits Needed in Calculus? Amer. Math. Monthly 118 (2011), 404-417.
  8. Some landmarks in the history of the tangential Cauchy-Riemann equations. Rendiconti di Matematica, Serie VII, 30 (2010) , 275-283.
  9. On Antiderivatives of the Zero Function. Mathematics Magazine 80 (2007), 387 - 390
  10. 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
  11. 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.
  12. Complex Analysis: A Brief Tour into Higher Dimensions, Amer. Math. Monthly 110 (2003), 89 - 108.
  13. (Selected for the 2004 Lester R. Ford Award of the Mathematical Association of America.)
  14. Extension Phenomena in Multidimensional Complex Analysis: Correction of the Historical Record. The Mathematical Intelligencer 24, no 2 (2002), 4 - 12
  15. On d-bar Problems on (Pseudo) - Convex Domains. Topics in Complex Analysis, Banach Center Publ. 31, 311 - 320, Polish Acad. of Sci., Warszawa 1995
  16. Integral Kernels and H�lder Estimates for d-bar on pseudoconvex domains of finite type in C^2. Math. Ann. 288 (1990), 63 - 74
  17. 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
  18. Integral Representations and Estimates in the Theory of the d-bar Neumann Problem. (with I. Lieb) Ann. of Math. 123 (1986), 265 - 301