Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
As a somewhat amusing and personal note, I should mention that in the late 1980s I had founded a small publishing company in southern Italy, Mediterranean Press was its name; at that time Ehrenpreis was visiting my department, and he had accepted my invitation to write a book on the Radon transform for my company. During the next several years, I therefore saw several preliminary versions of the book, but by the mid-1990s I had left Italy, sold my equity in the company, and Ehrenpreis had found a much more appropriate outlet for his work.
References
Berenstein, C.A., Dostal, M.: Analytically Uniform Spaces and Their Applications to Convolution Equations. Springer Lecture Notes in Mathematics, vol. 256. Springer, Berlin (1972)
Berenstein, C.A., Struppa, D.C.: On the Fabry–Ehrenpreis–Kawai gap theorem. Publ. Res. Inst. Math. Sci. 23, 565–574 (1987)
Berenstein, C.A., Struppa, D.C.: Dirichlet series and convolution equations. Publ. Res. Inst. Math. Sci. 24, 783–810 (1988)
Berenstein, C.A., Kawai, T., Struppa, D.C.: Interpolation varieties and the Fabry–Ehrenpreis–Kawai gap theorem. Adv. Math. 122, 280–310 (1996)
Berenstein, C.A., Taylor, B.A.: Interpolation problems in ℂn with applications to harmonic analysis. J. Anal. Math. 38, 188–254 (1980)
Ehrenpreis, L.: Solutions of some problems of division I. Am. J. Math. 76, 883–903 (1954)
Ehrenpreis, L.: A new proof and an extension of Hartogs’ theorem. Bull. Am. Math. Soc. 67, 507–509 (1961)
Ehrenpreis, L.: Fourier Analysis in Several Complex Variables. Wiley-Interscience, New York (1970)
Ehrenpreis, L.: Edge of the wedge theorem for partial differential equations. Harmonic analysis in Euclidean spaces. Proc. Symp. Pure Math. XXXV, 203–212 (1979)
Ehrenpreis, L.: Reflection, removable singularities, and approximation for partial differential equations. I. Ann. Math. 112, 1–20 (1980)
Ehrenpreis, L.: The edge-of-the-wedge theorem for partial differential equations. Ann. Math. Stud. 100, 155–169 (1981)
Ehrenpreis, L.: Spectral gaps and lacunas. Bull. Sci. Math. 105, 17–28 (1981)
Ehrenpreis, L.: Reflection, removable singularities, and approximation for partial differential equations. II. Trans. Am. Math. Soc. 302, 1–45 (1987)
Ehrenpreis, L.: Extensions of solutions of partial differential equations. Geometrical and algebraical aspects in several complex variables. Semin. Conf. 8, 361–375 (1991)
Ehrenpreis, L.: The Universality of the Radon Transform. With an Appendix by Peter Kuchment and Eric Todd Quinto. Oxford University Press, New York (2003)
Ehrenpreis, L.: Some novel aspects of the Cauchy problem. Harmonic analysis, signal processing, and complexity. Prog. Math. 238, 1–14 (2005)
Hartogs, F.: Einige Folgerungen aux Cauchyschen Integralformel bei Funktionen Mehrer Veranderlichen. Munch. Sitzungber. 36, 223–241 (1906)
Kawai, T.: The Fabry–Ehrenpreis gap theorem for hyperfunctions. Proc. Jpn. Acad., Ser. A, Math. Sci., 60, 276–278 (1984)
Kawai, T.: The Fabry–Ehrenpreis gap theorem and systems of linear differential equations of infinite order. Am. J. Math. 109, 57–64 (1987)
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)
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)
Levinson, N.: Gap and Density Theorems. Am. Math. Society, New York (1940)
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)
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)
Palamodov, V.P.: Linear Differential Operators with Constant Coefficients. Springer, Berlin (1970)
Range, R.M.: Extension phenomena in multidimensional complex analysis: Correction of the historical record. Math. Intell. 24, 4–12 (2002)
Struppa, D.C.: The fundamental principle for systems of convolution equations. Mem. Am. Math. Soc. 283, 1–167 (1981)
Struppa, D.C.: The first eighty years of Hartogs’ theorem. In: Geometry Seminars, pp. 127–209. Univ. Stud. Bologna, Bologna (1988)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Italia
About this paper
Cite this paper
Struppa, D.C. (2012). Leon Ehrenpreis, a Unique Mathematician. In: Sabadini, I., Struppa, D. (eds) The Mathematical Legacy of Leon Ehrenpreis. Springer Proceedings in Mathematics, vol 16. Springer, Milano. https://doi.org/10.1007/978-88-470-1947-8_2
Download citation
DOI: https://doi.org/10.1007/978-88-470-1947-8_2
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1946-1
Online ISBN: 978-88-470-1947-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)