Leon Ehrenpreis, Recollections from the Recent Decades

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 16)


Leon Ehrenpreis was an outstanding world-class mathematician and a wonderful, warm person. I had a privilege to consider myself his friend for the last two decades. It is hard to do justice to his manifold mathematics and personality, but I will try to at least add some recollections to this tribute volume.


Single Photon Emission Compute Tomography Convex Body Integral Geometry Poisson Summation Formula Poincare Series 
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.
    Agranovsky, M.: CR foliations, the strip-problem and Globevnik–Stout conjecture. C. R. Math. 343(2), 91–94 (2006) MathSciNetMATHGoogle Scholar
  2. 2.
    Agranovsky, M.: Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs. Adv. Math. 211(1), 284–326 (2007) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Agranovsky, M., Berenstein, C.A., Kuchment, P.: Approximation by spherical waves in L p-spaces. J. Geom. Anal. 6(3), 365–383 (1996) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Agranovsky, M., Globevnik, J.: Analyticity on circles for rational and real analytic functions of two real variables. J. Anal. Math. 91, 31–65 (2003) MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Agranovsky, M., Kuchment, P., Kunyansky, L.: On reconstruction formulas and algorithms for the thermoacoustic and photoacoustic tomography. In: Wang, L.H. (ed.) Photoacoustic Imaging and Spectroscopy, pp. 89–101. CRC Press, Boca Raton (2009) CrossRefGoogle Scholar
  6. 6.
    Agranovsky, M., Narayanan, E.: Isotopic families of contact manifolds for elliptic PDE. Proc. Am. Math. Soc. 134(7), 2117–2123 (2006) MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Agranovsky, M.L., Quinto, E.T.: Injectivity sets for the Radon transform over circles and complete systems of radial functions. J. Funct. Anal. 139, 383–413 (1996) MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Aguilar, V., Ehrenpreis, L., Kuchment, P.: Range condition for the exponential Radon transform. J. Anal. Math. 68, 1–13 (1996) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Akhiezer, N.I., Ronkin, L.I.: On separately analytic functions of several variables and theorems on “the edge of the wedge”. Russ. Math. Surv. 28(3), 27–42 (1973) CrossRefGoogle Scholar
  10. 10.
    Bal, G., Finch, D., Kuchment, P., Schotland, J., Stefanov, P., Uhlmann, G. (eds.) Tomography and Inverse Transport Theory. Contemp. Math., vol. 559, Am. Math. Soc., Providence (2011) MATHGoogle Scholar
  11. 11.
    Ehrenpreis, L.: Special functions. Inverse Probl. Imaging 4(4), 639–647 (2010) MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Ehrenpreis, L.: Microglobal analysis. Adv. Nonlinear Stud. 10(3), 729–739 (2010) MathSciNetMATHGoogle Scholar
  13. 13.
    Ehrenpreis, L.: Eisenstein and Poincaré series on SL(3,ℝ). Int. J. Number Theory 5(8), 1447–1475 (2009) MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Ehrenpreis, L.: The Radon transform for functions defined on planes. In: Integral Geometry and Tomography. Contemp. Math., vol. 405, pp. 41–46. Am. Math. Soc., Providence (2006) CrossRefGoogle Scholar
  15. 15.
    Ehrenpreis, L.: Some novel aspects of the Cauchy problem. In: Harmonic Analysis, Signal Processing, and Complexity. Progr. Math., vol. 238, pp. 1–14. Birkhäuser Boston, Boston (2005) CrossRefGoogle Scholar
  16. 16.
    Ehrenpreis, L.: The role of Paley–Wiener theory in partial differential equations. In: The Legacy of Norbert Wiener: A Centennial Symposium, Cambridge, MA, 1994. Proc. Sympos. Pure Math., vol. 60, pp. 71–83. Am. Math. Soc., Providence (1997) Google Scholar
  17. 17.
    Ehrenpreis, L.: Parametric and nonparametric Radon transform. In: 75 Years of Radon Transform, Vienna, 1992. Conf. Proc. Lecture Notes Math. Phys., vol. IV, pp. 110–122. Int. Press, Cambridge (1994) Google Scholar
  18. 18.
    Ehrenpreis, L.: Some Nonlinear Aspects of the Radon Transform, Tomography, Impedance Imaging, and Integral Geometry (South Hadley, MA, 1993). Lectures in Appl. Math., vol. 30, pp. 69–81. Am. Math. Soc., Providence (1994) Google Scholar
  19. 19.
    Ehrenpreis, L.: Singularities, Functional Equations, and the Circle Method. The Rademacher Legacy to Mathematics (University Park, PA, 1992). Contemp. Math., vol. 166, pp. 35–80. Am. Math. Soc., Providence (1994) Google Scholar
  20. 20.
    Ehrenpreis, L.: Exotic parametrization problems. Ann. Inst. Fourier (Grenoble) 4(5), 1253–1266 (1993) MathSciNetCrossRefGoogle Scholar
  21. 21.
    Ehrenpreis, L.: Function theory for Rogers–Ramanujan-like partition identities. In: A Tribute to Emil Grosswald: Number Theory and Related Analysis. Contemp. Math., vol. 143, pp. 259–320. Am. Math. Soc., Providence (1993) CrossRefGoogle Scholar
  22. 22.
    Ehrenpreis, L.: The Schottky relation in genus 4. In: Curves, Jacobians, and Abelian varieties, Amherst, MA, 1990. Contemp. Math., vol. 136, pp. 139–160. Am. Math. Soc., Providence (1992) CrossRefGoogle Scholar
  23. 23.
    Ehrenpreis, L.: Extensions of solutions of partial differential equations. In: Geometrical and Algebraical Aspects in Several Complex Variables, Cetraro, 1989. Sem. Conf., vol. 8, pp. 361–375. EditEl, Rende (1991) Google Scholar
  24. 24.
    Ehrenpreis, L.: Hypergeometric functions. In: Special Functions (Okayama, 1990), ICM-90 Satell. Conf. Proc, pp. 78–89. Springer, Tokyo (1991) CrossRefGoogle Scholar
  25. 25.
    Ehrenpreis, L.: Lewy unsolvability and several complex variables. Mich. Math. J. 38(3), 417–439 (1991) MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Ehrenpreis, L.: The Radon transform and tensor products. In: Integral Geometry and Tomography, Arcata, CA, 1989. Contemp. Math., vol. 113, pp. 57–63. Am. Math. Soc., Providence (1990) CrossRefGoogle Scholar
  27. 27.
    Ehrenpreis, L.: Three Problems at Mount Holyoke. Contemp. Math., vol. 278. Am. Math. Soc., Providence (2001) Google Scholar
  28. 28.
    Ehrenpreis, L.: The Universality of the Radon Transform. Oxford Univ. Press, London (2003) MATHCrossRefGoogle Scholar
  29. 29.
    Ehrenpreis, L., Kuchment, P., Panchenko, A.: The exponential X-ray transform and Fritz John’s equation. I. Range description. In: Analysis, Geometry, Number Theory: the Mathematics of Leon Ehrenpreis (Philadelphia, PA, 1998). Contemporary Math., vol. 251, pp. 173–188. Am. Math. Soc., Providence (2000) CrossRefGoogle Scholar
  30. 30.
    Farkas, H., Kawai, T., Kuchment, P., Quinto, T.E., Sternberg, S., Struppa, D., Taylor, B.A.: Remembering Leon Ehrenpreis: 1930–2010. Not. Am. Math. Soc. 58(5), 674–681 (2011) MathSciNetMATHGoogle Scholar
  31. 31.
    Finch, D., Patch, S., Rakesh: Determining a function from its mean values over a family of spheres. SIAM J. Math. Anal. 35(5), 1213–1240 (2004) MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    Finch, D., Rakesh: The spherical mean value operator with centers on a sphere. Inverse Probl. 23(6), S37–S50 (2007) MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Finch, D., Rakesh: Recovering a function from its spherical mean values in two and three dimensions. In: Photoacoustic Imaging and Spectroscopy. CRC Press, Boca Raton (2009) Google Scholar
  34. 34.
    Gelfand, I., Gindikin, S., Graev, M.: Integral geometry in affine and projective spaces. J. Sov. Math. 18, 39–167 (1980) CrossRefGoogle Scholar
  35. 35.
    Gelfand, I., Gindikin, S., Graev, M.: Selected Topics in Integral Geometry. Transl. Math. Monogr., vol. 220. Am. Math. Soc., Providence (2003) MATHGoogle Scholar
  36. 36.
    Gelfand, I., Graev, M., Vilenkin, N.: Generalized Functions. Integral Geometry and Representation Theory, vol. 5. Academic Press, San Diego (1965) Google Scholar
  37. 37.
    Globevnik, J.: Testing analyticity on rotation invariant families of curves. Trans. Am. Math. Soc. 306, 401–410 (1988) MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Globevnik, J.: Analyticity on translates of a Jordan curve. Trans. Am. Math. Soc. 359, 5555–5565 (2007) MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    Guillemin, V.: Fourier Integral Operators from the Radon Transform Point of View. Proc. Symposia in Pure Math., vol. 27, pp. 297–300 (1975) Google Scholar
  40. 40.
    Guillemin, V.: On Some Results of Gelfand in Integral Geometry. Proc. Symposia in Pure Math., vol. 43, pp. 149–155 (1985) Google Scholar
  41. 41.
    Guillemin, V., Sternberg, S.: Geometric Asymptotics. Am. Math. Soc., Providence (1977) MATHGoogle Scholar
  42. 42.
    Helgason, S.: The Radon Transform. Birkhäuser, Basel (1980) MATHCrossRefGoogle Scholar
  43. 43.
    Helgason, S.: Groups and Geometric Analysis. Am. Math. Soc., Providence (2000) MATHGoogle Scholar
  44. 44.
    Helgason, S.: Geometric Analysis on Symmetric Spaces. AMS, Providence (2008) MATHGoogle Scholar
  45. 45.
    Helgason, S.: Integral Geometry and Radon Transforms. Springer, Berlin (2010) Google Scholar
  46. 46.
    John, F.: Plane Waves and Spherical Means, Applied to Partial Differential Equations. Dover, New York (1971) Google Scholar
  47. 47.
    Kuchment, P., Kunyansky, L.: Mathematics of thermoacoustic and photoacoustic tomography. Eur. J. Appl. Math. 19(2), 191–224 (2008) MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    Kuchment, P., Lvin, S.: Paley–Wiener theorem for exponential Radon transform. Acta Appl. Math. 18, 251–260 (1990) MathSciNetMATHCrossRefGoogle Scholar
  49. 49.
    Kuchment, P., Lvin, S.: The range of the exponential Radon transform. Sov. Math. Dokl. 42(1), 183–184 (1991) MathSciNetGoogle Scholar
  50. 50.
    Kuchment, P., Lvin, S.: Identities for sinx that came from medical imaging. Preprint, arXiv:1110.6109
  51. 51.
    Kuchment, P., Quinto, E.T.: Some problems of integral geometry arising in tomography. In: The Universality of the Radon Transform. Oxford Univ. Press, London (2003) Google Scholar
  52. 52.
    Natterer, F.: The Mathematics of Computerized Tomography. Wiley, New York (1986) MATHGoogle Scholar
  53. 53.
    Natterer, F., Wübbeling, F.: Mathematical Methods in Image Reconstruction. Monographs on Mathematical Modeling and Computation, vol. 5. SIAM, Philadelphia (2001) MATHCrossRefGoogle Scholar
  54. 54.
    Öktem, O.: Extension of separately analytic functions and applications to range characterization of the exponential Radon transform. Ann. Pol. Math. 70, 195–213 (1998) MATHGoogle Scholar
  55. 55.
    Palamodov, V.P.: Reconstructive Integral Geometry. Birkhäuser, Basel (2004) MATHCrossRefGoogle Scholar
  56. 56.
    Sharafutdinov, V.A.: Integral Geometry of Tensor Fields. V.S.P. Intl Science (1994) Google Scholar
  57. 57.
    Tumanov, A.: A Morera type theorem in the strip. Math. Res. Lett. 11, 23–29 (2004) MathSciNetMATHGoogle Scholar
  58. 58.
    Tumanov, A.: Testing analyticity on circles. Am. J. Math. 129(3), 785–790 (2007) MathSciNetMATHCrossRefGoogle Scholar
  59. 59.
    Tumanov, A.: Analytic continuation from a family of lines. J. Anal. Math. 105, 391–396 (2008) MathSciNetMATHCrossRefGoogle Scholar
  60. 60.
    Wang, L. (ed.): Photoacoustic Imaging and Spectroscopy. CRC Press, Boca Raton (2009) Google Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.Texas A&M UniversityCollege StationUSA

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