R. Michael Range

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

SELECTED RECENT INVITED LECTURES

Ph.D. STUDENTS

PUBLICATIONS

BOOKS:

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

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

SELECTED RECENT ARTICLES:

  1. A Pointwise a-priori Estimate for the d-bar Neumann Problem on Weakly Pseudoconvex Domains. Pacific J. Math. 275 (2015), 409 - 432.
  2. Descartes's Double Point Method for Tangents: An Old Idea Suggests New Approaches to Calculus. Notices Amer. Math. Soc. 61(4) (2014), 387-389.
  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