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Interpolation theorems in several complex variables and applications

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1540)

Keywords

  • Holomorphic Function
  • Entire Function
  • Linear Differential Equation
  • Dirichlet Series
  • Interpolation Problem

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References

  1. C.A. Berenstein, T. Kawai and D.C. Struppa, Interpolating varieties and the Fabry-Ehrenpreis-Kawai gap theorem, forthcoming.

    Google Scholar 

  2. C.A. Berenstein and D.C. Struppa, On the Ehrenpreis-Kawai gap Theorem, Publ R.I.M.S. Kyoto University 23 (1987), 565–574.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. C.A. Berenstein and D.C. Struppa, Convolution equations and Dirichlet series, Publ. R.I.M.S. Kyoto University 24 (1988), 783–810

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. C.A. Berenstein and B.A. Taylor, Interpolations problems in Cn with applications to harmonic analysis, J. Analyse Math. 38 (1980),188–254.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. R.P. Boas, Entire Functions, Academic Press, 1959.

    Google Scholar 

  6. L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Wiley-Interscience, New York, 1970.

    MATH  Google Scholar 

  7. L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966.

    MATH  Google Scholar 

  8. A. Kaneko, On continuation of regular solutions of partial differential equations to compact convex sets II, J. Fac. Sci. Univ. Tokyo 18 (1971),415–433.

    MATH  Google Scholar 

  9. M. Kashiwara and T. Kawai, A differential relation between ϑ(t+a) and ϑ(t), RIMS Technical Report No 485, RIMS, Kyoto University. (1984)

    Google Scholar 

  10. M. Kashiwara, T. Kawai and Y. Takei, The structure of cohomology groups associated with the theta-zerovalues, in Proc. of “Algebraical and Geometrical Aspects in Several Complex Variables”, Cetraro 1989, C.A. Berenstein and D.C. Struppa eds.

    Google Scholar 

  11. T. Kawai, The Fabry-Ehrenpreis gap Theorem for hyperfunctions, Proc Japan Acad. 60 A (1984), 276–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. T. Kawai, The Fabry-Ehrenpreis gap theorem and linear differential equations of infinite order, Amer. J. Math. 109 (1987), 57–64.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. T. Kawai, An example of a complex of linear differential operators of infinite order, Proc. Japan Acad. 59A (1983),113–115.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. T. Kawai, Some remarks on microlocal analysis of ϑ-functions, Suken-kokyuroku, no. 410, RIMS, Kyoto University, 76–87,(1980), (in Japanese).

    Google Scholar 

  15. T. Kawai and D.C. Struppa, On the existence of holomorphic solutions of systems of linear differential equations of infinite order and with constant coefficients, Int. J. Math. 1 (1990), 83–82.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. T. Kawai and Y. Takei, “Fundamental Principle” and ϑ-zerovalue, Sukenkokyuroku, no. 675, RIMS, Kyoto University, 79–86 (1988), (in Japanese).

    Google Scholar 

  17. N. Levinson, Gap and Density Theorems, A.M.S.,1940

    Google Scholar 

  18. M. Sato, Pseudo-differential equations and theta function, Astérisque 2–3 (1973), 286–291.

    MATH  Google Scholar 

  19. M. Sato, M. Kashiwara and T. Kawai, Linear differential equations of infinite order and theta functions, Advances in Math. 47 (1983),300–325.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. M. Sato, M. Kashiwara and T. Kawai, Microlocal analysis of theta functions, Adv. Studies in Pure Math. 4 (1984) 267–289.

    MathSciNet  MATH  Google Scholar 

  21. M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, Lecture Notes in Math. 286, Springer, Berlin-Heidelberg-New York, 1973, 265–529.

    MATH  Google Scholar 

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Dedicated to the memory of the late Professor Kôsaku Yosida

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© 1993 Springer-Verlag

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Berenstein, C.A., Kawai, T., Struppa, D.C. (1993). Interpolation theorems in several complex variables and applications. In: Komatsu, H. (eds) Functional Analysis and Related Topics, 1991. Lecture Notes in Mathematics, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085470

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  • DOI: https://doi.org/10.1007/BFb0085470

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56471-3

  • Online ISBN: 978-3-540-47565-1

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