Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-24T09:16:10.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Problèmes d’Interpolation dans des Espaces d’Ultradistributions de Type Roumieu

Published online by Cambridge University Press:  22 January 2016

Alex Meril
Alex Meril*
Affiliation:
Université Antilles Guyane, U.F.R. Sciences Department de Mathématiques B. P. N° 592 97167 Pointe-à-Pitre Cedex, Guadeloupe
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Nous avons étudié en [12] des problèmes d’interpolation dans des espaces de fonctions holomorphes sur un cône ouvert convexe de sommet l’origine dans Cn, la croissance de ces fonctions étant contrôlée à l’infini. Nous nous intéressons maintenant à un espace plus petit en imposant en outre un contrôle de croissance à l’origine dans le cas où le cône est strict.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 129 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Berenstein, C. A. and Taylor, B. A., A new look at interpolation theory for entire functions of one variable, Adv. in Math., 33 (1979), 109–143.Google Scholar
[ 2 ] Berenstein, C. A. and Taylor, B. A., Interpolation problems in Cn with application to harmonic analysis, J. Anal. Math., 38 (1980), 188–254.Google Scholar
[ 3 ] Berenstein, C. A. and Struppa, D., Interpolation problems in cones Rendi Conti Acad, del Lincei, Serie VIII Vol. LXXIV fase. 5 Mai 1983, 267–273 Ibidem: VIII Vol. LXXIV fase. 6 Juin 1983, 331–335 Google Scholar
[ 4 ] Ehrenpreis, L., Fourier analysis in several complex variables Wiley Interscience, New-York 1970.Google Scholar
[ 5 ] Gurevich, D. I., Counterexample to a problem of L. Schwartz, Funct. Anal. Appl., 9 (1975),116–120.CrossRefGoogle Scholar
[ 6 ] Hörmander, L., L2 -estimates and existence theorem for the d operator, Acta Math., 113 (1965), 89–152.Google Scholar
[ 7 ] Hörmander, L., Generator for some rings of analytic functions, Bull. Amer. Math. Soc, 73 (1967), 943–949.Google Scholar
[ 8 ] Hörmander, L., Complex analysis in several variables, North-Holland, New-York, 1973.Google Scholar
[ 9 ] Kawai, T., On the theory of Fourier hyperfunctions and its application to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo Sect. IA., 17 (1970), 467–483.Google Scholar
[10] Kelleher, J. J., and Taylor, B. A., Finitely generated ideal in rings of analytic functions, Math. Ann., 193 (1971), 225–237.Google Scholar
[11] Meril, A., Analytic functions with unbounded carriers and mean periodic functions, Trans. Amer. Math. Soc, 278, no. 1 (1983), 115–136.Google Scholar
[12] Meril, A., Problèmes d’interpolation dans quelques espaces de fonctions non entières, Bull. Soc. Math. Fr., t. 111 (1983), 251–285.CrossRefGoogle Scholar
[13] Palamodov, V., Linear differential operator with constant coefficients, Springer Verlag, 1970.Google Scholar
[14] Rockafellar, R. T., Convex analysis, Princeton University Press, 1970.Google Scholar
[15] Roever, J. W. de, Fourier transform of holomorphic functions and application to Newton interpolation series II T. W. 148 Math. Centrum Amsterdam.Google Scholar
[16] Roever, J. W. de, Complex Fourier transform and analytic functions with unbounded carriers, Math. Centre Tracts 89, Amsterdam 1978.Google Scholar
[17] Saburi, Y., Vanishing theorems of cohomology groups with values in the sheaves Oinc and Odec, Tokyo J. Math., 5, no. 1 (1982), 225–248.Google Scholar
[18] Skoda, H., Application des techniques L2 à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids, Ann. Ec. Norm. Sup, 5(4) (1972), 545–579.Google Scholar
[19] Struppa, D., The fundamental principle for systems of convolutions equations, Mem. Amer. Math. Soc, 41, no. 273 (1983).Google Scholar