Arkiv för Matematik

  • Ark. Mat.
  • Volume 12, Number 1-2 (1974), 267-280.

The Ritt theorem in several variables

C. A. Berenstein and M. A. Dostal

Full-text: Open access

Note

The authors wish to thank Instituto de Matematica Pura e Aplicada, Rio de Janeiro, for its support and hospitality.

Article information

Source
Ark. Mat., Volume 12, Number 1-2 (1974), 267-280.

Dates
Received: 4 February 1974
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485896208

Digital Object Identifier
doi:10.1007/BF02384763

Mathematical Reviews number (MathSciNet)
MR377111

Zentralblatt MATH identifier
0293.33001

Rights
1974 © Institut Mittag-Leffler

Citation

Berenstein, C. A.; Dostal, M. A. The Ritt theorem in several variables. Ark. Mat. 12 (1974), no. 1-2, 267--280. doi:10.1007/BF02384763. https://projecteuclid.org/euclid.afm/1485896208


Export citation

References

  • Avanissian, V., Oral communication, 1970.
  • Berenstein, C. A. & Dostal, M. A., Analytically uniform spaces and their applications to convolution equations, Lecture Notes in Math., Vol. 256, Springer-Verlag (1972).
  • ——, Sur une classe de functions entières, C. R. Acad. Sci. Paris, 274 (1972), 1149–1152.
  • ——, Some remarks on convolution equations, Ann. Inst. Fourier (Grenoble), 23 (1973), 55–74.
  • ——, On convolution equations I, “L’Analyse harmonique dans le domaine complexe”, Lecture Notes in Math., Vol. 336, Springer-Verlag (1973), 79–94.
  • Berenstein, C. A. & Dostal, M. A., On convolution equations II, to appear in “Proceedings of the Conference on Analysis, Rio de Janeiro 1972”, (Hermann et Cie, Publ.).
  • ——, A lower estimate for exponential sums, Bull. Amer. Math. Soc. 80 (1974), 687–691; cf. also Prelim. Rep. 73T-B237 in Notices A.M.S. (August, 1973) p. A-492.
  • Dostal, M. A., An analogue of a theorem of Vladimir Bernstein and its applications to singular supports, Proc. London Math. Soc. 19 (1969), 553–576.
  • Ehrenpreis, L., Mean-periodic functions I, Amer. J. Math. 77 (1955), 293–328.
  • —, Fourier analysis in several complex variables, Wiley-Interscience, New York, 1970.
  • Fujiwara, M., Über den Mittelkörper zweier konvexen Körper, Sci. Rep. Res. Inst. Tôhoku Univ. 5 (1916), 275–283.
  • Hörmander, L., On the range of convolution operators, Ann. of Math. 76 (1962), 148–170.
  • —, Convolution equations in convex domains, Invent. Math. 4 (1968), 306–317.
  • Kiselman, C. O., On entire functions of exponential type and indicators of analytic functionals, Acta Math. 117 (1967), 1–35.
  • Laird, P. G., Some properties of mean periodic functions, J. Austral. Math. Soc. 14 (1972), 424–432.
  • Lax, P. D., The quotient of exponential polynomials, Duke Math. J. 15 (1948), 967–970.
  • Lelong, P., Fonctionnelles analytiques et fonctions entières (n variables), Les Presses de l’Univ. de Montréal, 1968.
  • Lindelöf, E., Sur les fonctions entières d’ordre entier, Ann. Sci. Ecole Norm. Sup. 22 (1905), 369–395.
  • Malgrange, B., Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble), 6 (1956), 271–335.
  • —, Sur les équations de convolution, Rend. Sem. Mat. Univ. e Politec. Torino 19 (1959/60), 19–27.
  • Martineau, A., Sur les fonctionnelles analytiques, J. Analyse Math. 11 (1963), 1–164.
  • Ritt, J. F., A factorization theory for functions $\sum a_i e^{\alpha _i x} $ , Trans. Amer. Math. Soc. 29 (1927), 584–596.
  • —, On the zeros of exponential polynomials, Trans. Amer. Math. Soc. 31 (1929), 680–686.
  • Selberg, H., Über einige transzendente Gleichungen, Avh. Norske Vid. Akad. Oslo, I/10 (1931), 1–8.
  • Shields, A., On quotients of exponential polynomials, Comm. Pure Appl. Math. 16 (1963), 27–31.
  • Trèves, F., Linear partial differential equations with constant coefficients, Gordon & Breach, 1966.
  • Kitagawa, K., Sur les polynômes exponentiels, J. Math. Kyoto Univ. 13 (1973), 489–496.
  • Avanissian, V. & Gay, R., Sur une transformation des fonctionnelles analytiques portables par des convexes compacts de Cd, et la convolution d’Hadamard, C. R. Acad. Sci., Paris, 279 (1974), 133–136.
  • ——, Sur les fonctions entières arithmétiques de type exponentiel et le quotient d’exponentielle-polynômes de plusieures variables—(ibidem)..