Leon Ehrenpreis, a Unique Mathematician

  • Daniele C. Struppa
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 16)


What made Ehrenpreis’ mathematics so unique was his bold approach to classical problems, and his interest in finding an overarching and unifying framework for a variety of apparently unrelated problems. In this note I will try to highlight this characteristic, by looking at some of Ehrenpreis’ papers which are not, strictly speaking, connected with either the Fundamental Principle or the Radon Transform.


Holomorphic Function Dirichlet Series Overdetermined System Convolution Equation Radon Transform 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Berenstein, C.A., Dostal, M.: Analytically Uniform Spaces and Their Applications to Convolution Equations. Springer Lecture Notes in Mathematics, vol. 256. Springer, Berlin (1972) MATHGoogle Scholar
  2. 2.
    Berenstein, C.A., Struppa, D.C.: On the Fabry–Ehrenpreis–Kawai gap theorem. Publ. Res. Inst. Math. Sci. 23, 565–574 (1987) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Berenstein, C.A., Struppa, D.C.: Dirichlet series and convolution equations. Publ. Res. Inst. Math. Sci. 24, 783–810 (1988) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Berenstein, C.A., Kawai, T., Struppa, D.C.: Interpolation varieties and the Fabry–Ehrenpreis–Kawai gap theorem. Adv. Math. 122, 280–310 (1996) MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Berenstein, C.A., Taylor, B.A.: Interpolation problems in ℂn with applications to harmonic analysis. J. Anal. Math. 38, 188–254 (1980) MathSciNetMATHGoogle Scholar
  6. 6.
    Ehrenpreis, L.: Solutions of some problems of division I. Am. J. Math. 76, 883–903 (1954) MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Ehrenpreis, L.: A new proof and an extension of Hartogs’ theorem. Bull. Am. Math. Soc. 67, 507–509 (1961) MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Ehrenpreis, L.: Fourier Analysis in Several Complex Variables. Wiley-Interscience, New York (1970) MATHGoogle Scholar
  9. 9.
    Ehrenpreis, L.: Edge of the wedge theorem for partial differential equations. Harmonic analysis in Euclidean spaces. Proc. Symp. Pure Math. XXXV, 203–212 (1979) MathSciNetGoogle Scholar
  10. 10.
    Ehrenpreis, L.: Reflection, removable singularities, and approximation for partial differential equations. I. Ann. Math. 112, 1–20 (1980) MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Ehrenpreis, L.: The edge-of-the-wedge theorem for partial differential equations. Ann. Math. Stud. 100, 155–169 (1981) MathSciNetGoogle Scholar
  12. 12.
    Ehrenpreis, L.: Spectral gaps and lacunas. Bull. Sci. Math. 105, 17–28 (1981) MathSciNetMATHGoogle Scholar
  13. 13.
    Ehrenpreis, L.: Reflection, removable singularities, and approximation for partial differential equations. II. Trans. Am. Math. Soc. 302, 1–45 (1987) MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Ehrenpreis, L.: Extensions of solutions of partial differential equations. Geometrical and algebraical aspects in several complex variables. Semin. Conf. 8, 361–375 (1991) MathSciNetGoogle Scholar
  15. 15.
    Ehrenpreis, L.: The Universality of the Radon Transform. With an Appendix by Peter Kuchment and Eric Todd Quinto. Oxford University Press, New York (2003) Google Scholar
  16. 16.
    Ehrenpreis, L.: Some novel aspects of the Cauchy problem. Harmonic analysis, signal processing, and complexity. Prog. Math. 238, 1–14 (2005) MathSciNetGoogle Scholar
  17. 17.
    Hartogs, F.: Einige Folgerungen aux Cauchyschen Integralformel bei Funktionen Mehrer Veranderlichen. Munch. Sitzungber. 36, 223–241 (1906) Google Scholar
  18. 18.
    Kawai, T.: The Fabry–Ehrenpreis gap theorem for hyperfunctions. Proc. Jpn. Acad., Ser. A, Math. Sci., 60, 276–278 (1984) MATHCrossRefGoogle Scholar
  19. 19.
    Kawai, T.: The Fabry–Ehrenpreis gap theorem and systems of linear differential equations of infinite order. Am. J. Math. 109, 57–64 (1987) MATHCrossRefGoogle Scholar
  20. 20.
    Kawai, T., Struppa, D.C.: On the existence of holomorphic solutions of systems of linear differential equations of infinite order and with constant coefficients. Int. J. Math. 1, 63–82 (1990) MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Kawai, T., Struppa, D.C.: Overconvergence phenomena and grouping in exponential representation of solutions of linear differential equations of infinite order. Adv. Math. 161, 131–140 (2001) MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Levinson, N.: Gap and Density Theorems. Am. Math. Society, New York (1940) Google Scholar
  23. 23.
    Malgrange, B.: Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution. Ann. Inst. Fourier (Grenoble) 6, 271–355 (1956) MathSciNetCrossRefGoogle Scholar
  24. 24.
    Meril, A., Struppa, D.C.: Phénomène de Hartogs et équations de convolution. Séminaire d’Analyse P. Lelong–P. Dolbeault–H. Skoda, Années 1985/1986. Springer Lecture Notes in Math., vol. 1295, pp. 146–156. Springer, Berlin (1987) Google Scholar
  25. 25.
    Palamodov, V.P.: Linear Differential Operators with Constant Coefficients. Springer, Berlin (1970) MATHCrossRefGoogle Scholar
  26. 26.
    Range, R.M.: Extension phenomena in multidimensional complex analysis: Correction of the historical record. Math. Intell. 24, 4–12 (2002) MathSciNetCrossRefGoogle Scholar
  27. 27.
    Struppa, D.C.: The fundamental principle for systems of convolution equations. Mem. Am. Math. Soc. 283, 1–167 (1981) Google Scholar
  28. 28.
    Struppa, D.C.: The first eighty years of Hartogs’ theorem. In: Geometry Seminars, pp. 127–209. Univ. Stud. Bologna, Bologna (1988) Google Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.Schmid College of Science and TechnologyChapman UniversityOrangeUSA

Personalised recommendations