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Interpolation problems in Cn with applications to harmonic analysis

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References

  1. E. Bedford and T. Kawai,Local extension of solutions of systems of linear differential equations with constant coefficients. Comm. Pure Appl. Math.30 (1977), 235–254.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. A. Berenstein and M. Dostal,Analytically Uniform Spaces and Their Applications to Convolution Equations, Lecture Notes in Math.256, Springer-Verlag, New York, 1972.

    MATH  Google Scholar 

  3. C. A. Berenstein and M. Dostal,A lower estimate for exponential sums, Bull. Amer. Math. Soc.80 (1974), 687–692.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. A. Berenstein and B. A. Taylor,The “three squares” theorem for continuous functions, Arch. Rational Mech. Anal.63 (1977), 253–259.

    Article  MATH  MathSciNet  Google Scholar 

  5. C. A. Berenstein and B. A. Taylor,A new look at interpolation theory for entire functions of one variable, Advances in Math.33 (1979), 109–143.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. A. Berenstein and B. A. Taylor,Mean-periodic functions, preprint.

  7. R. P. Boas,Entire Functions, Academic Press, New York, 1954.

    MATH  Google Scholar 

  8. A. I. Borisevich and G. P. Lapin,On the interpolation of entire functions, Sibirsk Mat. Ž.9 (1968), 522–529.

    MathSciNet  Google Scholar 

  9. L. Brown, B. Schreiber and B. Taylor,Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier (Grenoble)23 (1973), 125–154.

    MathSciNet  Google Scholar 

  10. J. Delsarte,Note sur une propriété nouvelle des fonctions harmoniques, C. R. Acad. Sci. Paris246 (1958), 1358–1360.

    MATH  MathSciNet  Google Scholar 

  11. J. Delsarte,Théorie des fonctions moyenne-périodiques de deux variables, Ann. of Math.72 (1960), 121–178.

    Article  MathSciNet  Google Scholar 

  12. L. Ehrenpreis,Solution of some problems of division. Part IV. Invertible and elliptic operators, Amer. J. Math.76 (1960), 522–588.

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  14. L. Ehrenpreis and P. Malliavin,Invertible operators and interpolation in AU spaces, J. Math. Pure Appl.53 (1974), 165–182.

    MATH  MathSciNet  Google Scholar 

  15. H. Federer,Geometric Measure Theory, Springer-Verlag, New York, 1969.

    MATH  Google Scholar 

  16. A. M. Gleason,The Cauchy-Weil theorem, J. Math. Mech.12 (1963), 429–444.

    MATH  MathSciNet  Google Scholar 

  17. P. A. Griffiths,Variations on a theorem of Abel, Invent. Math.35 (1976), 321–380.

    Article  MATH  MathSciNet  Google Scholar 

  18. O. v. Grudzinski,Einige elementare Ungleichungen für Exponentialpolynome, Math. Ann.221 (1976), 9–34.

    Article  MATH  MathSciNet  Google Scholar 

  19. R. C. Gunning and H. Rossi,Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, NJ, 1965.

    MATH  Google Scholar 

  20. D. I. Gurevich,Generalized bases in certain rings of holomorphic functions, Math. USSR-Izv.6 (1972), 564–578.

    Article  MATH  Google Scholar 

  21. D. I. Gurevich,Closed ideals with exp-polynomial generators in rings of entire function of two variables, Izv. Akad. Nauk Armjan. SSR Ser. Mat.9 (1974) 459–472, 510; Math. Reviews52, #785 (Russian).

    Google Scholar 

  22. D. I. Gurevich,Counterexamples to a problem of L Schwartz, Functional Anal. Appl.9 (1975), 116–120.

    Article  MATH  Google Scholar 

  23. L. Hörmander,Generators for some rings of analytic functions, Bull. Amer. Math. Soc.73, (1967), 943–949.

    Article  MATH  MathSciNet  Google Scholar 

  24. L. Hörmander,Complex Analysis in Several Variables, North Holland/American Elsevier, New York, 1973.

    MATH  Google Scholar 

  25. C. G. J. Jacobi,Theoremata nova algebraica circa system a duarum aequationum inter duas variables propositarum, Gesammelte Werke, Band III, pp. 285–294.

  26. C. G. J. Jacobi,De relationibus, quae locum habere debent inter puncta intersectionis duarum curvarum vel trium superficierum algebraicarum dati ordinis, simul cum enodatione paradoxi algebraici, Gesammelte Werke, Band III, pp. 329–354.

  27. J. Kelleher and B. A. Taylor,Finitely generated ideals in rings of analytic functions, Math. Ann.193 (1971), 225–237.

    Article  MATH  MathSciNet  Google Scholar 

  28. H. Komatsu,An introduction to the theory of hyperfunctions, Springer-Verlag Lecture Notes in Mathematics287, 1971, pp. 3–40.

    MathSciNet  Google Scholar 

  29. A. F. Leont’ev,On properties of sequences of linear aggregates that converge in a region in which the system of functions generating the linear aggregates is not complete, Amer. Math. Soc. Transl.10 (1958), 1–12.

    MATH  MathSciNet  Google Scholar 

  30. B. Levin,Distribution of Zeros of Entire Functions, Transl. Math. Monographs, Vol. 5, Amer. Math. Soc., Providence, RI, 1964.

    MATH  Google Scholar 

  31. F. S. Macaulay,The Algebraic Theory of Modular Systems, Cambridge Tracts in Mathematics and Mathematical Physics, No. 19, Cambridge University Press, London, 1916.

    MATH  Google Scholar 

  32. B. Malgrange,Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble),6 (1955–56), 271–355.

    MathSciNet  Google Scholar 

  33. B. Malgrange,Sur les équations de convolution, Rend. Sem. Mat. Univ. e. Politec. Torino19 (1959–60), 19–27.

    MathSciNet  Google Scholar 

  34. A. Martineau,Distributions et valeurs au bord des fonctions holomorphes, in:Theory of Distributions, Proc. Inter. Summer Inst. Lisbon, 1964, pp. 193–326.

    Google Scholar 

  35. Y. Meyer,Remarques sur un théorème des J. Delsarte, Ann. Inst. Fourier (Grennoble)26 (1976), 133–152.

    MATH  Google Scholar 

  36. H. Muggli,Differentialgleichungen unendlich hoher ordnung mit konstanten koeffizienten, Comment Math. Helv.11 (1938–39), 151–179.

    Article  MathSciNet  Google Scholar 

  37. A. Owstrowski,Solutions of Equations in Euclidean and Banach Spaces, Academic Press, 1973.

  38. V. Palamadov,Linear Differential Operators with Constants Coefficients, Springer-Verlag, New York, 1970.

    Google Scholar 

  39. L. Schwartz,Théorie générale des fonctions moyenne-périodiques, Ann. of Math.48 (1947), 857–929.

    Article  MathSciNet  Google Scholar 

  40. L. Schwartz,Théorie des Distributions, Hermann, 1960.

  41. B. A. Taylor,Analytically uniform spaces of infinitely differentiable functions, Comm. Pure Appl. Math.24 (1971), 39–51.

    Article  MATH  MathSciNet  Google Scholar 

  42. G. Valiron,Sur les solutions des équations différentialles linéaires d’ordre infini et à coefficients constants, Ann. Sci. École Norm. Sup. (3),46 (1929), 25–53.

    MathSciNet  Google Scholar 

  43. B. L. Van der Waerden,Modern Algebra, Vols 1, 2, Frederick Ungar Publishing Co., New York, 1970.

    Google Scholar 

  44. H. Whitney,Complex Analytic Varieties, Addison-Wesley, Reading, Mass., 1972.

  45. A. Yger,Fonctions moyenne-périodiques de deux variables. Etude de systems d’équations de convolution envisages par J. Delsarte, preprint.

  46. L. Zalcman,Analyticity and the Pompeiu problem, Arch. Rational Mech. Anal.47 (1972).

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This work was supported in part by grants from the National Science Foundation.

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Berenstein, C.A., Taylor, B.A. Interpolation problems in Cn with applications to harmonic analysis. J. Anal. Math. 38, 188–254 (1980). https://doi.org/10.1007/BF03033881

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