Download PDF - The micro-support of the complex defined by a convolution operator in tube domainsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

The micro-support of the complex defined by a convolution operator in tube domains

Authors 1, 1

Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263 Japan

Bibliography

  1. [Ao] T. Aoki, Existence and continuation of holomorphic solutions of differential equations of infinite order, Adv. in Math. 72 (1988), 261-283.
  2. [BeGV] C. A. Berenstein, R. Gay and A. Vidras, Division theorems in the spaces of entire functions with growth conditions and their applications to PDE of infinite order, preprint.
  3. [BeSt] C. A. Berenstein and D. C. Struppa, A remark on 'convolutors in spaces of holomorphic functions', in: Lecture Notes in Math. 1276, Springer, 1987, 276-280.
  4. [BeSt] C. A. Berenstein and D. C. Struppa, Solutions of convolution equations in convex sets, Amer. J. Math. 109 (1987), 521-544.
  5. [BoS] J. M. Bony et P. Schapira, Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, Invent. Math. 17 (1972), 95-105.
  6. [E1] O. V. Epifanov, Solvability of convolution equations in convex domains, Mat. Zametki 15 (1974), 787-796 (in Russian); English transl.: Math. Notes 15 (1974), 472-477.
  7. [E2] O. V. Epifanov, On the surjectivity of convolution operators in complex domains, Mat. Zametki 16 (1974), 415-422. (in Russian); English transl.: Math. Notes 16 (1974), 837-841.
  8. [E3] O. V. Epifanov, Criteria for a convolution to be epimorphic in arbitrary regions of the complex plaine, Mat. Zametki 31 (1974), 695-705 (in Russian); English transl.: Math. Notes 31 (1982), 354-359.
  9. [F] Yu. Favorov, On the addition on the indicators of entire and subharmonic functions of several variables, Mat. Sb. 105 (147) (1978), 128-140 (in Russian).
  10. [H1] L. Hörmander, On the range of convoluton operators, Ann. of Math. 76 (1962), 148-170.
  11. [H2] L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, 1966.
  12. [I1] R. Ishimura, Théorèmes d'existence et d'approximation pour les équations aux dérivées partielles linéaires d'ordre infini, Publ. RIMS Kyoto Univ. 32 (1980), 393-415.
  13. [I2] R. Ishimura, Existence locale de solutions holomorphes pour les équations différentielles d'ordre infini, Ann. Inst. Fourier (Grenoble) 35 (3) (1985), 49-57.
  14. [I3] R. Ishimura, A remark on the characteristic set for convolution equations, Mem. Fac. Sci. Kyushu Univ. 46 (1992), 195-199.
  15. [IO] R. Ishimura and Y. Okada, The existence and the continuation of holomorphic solutions for convolution equations in tube domains, Bull. Soc. Math. France 122 (1994), 413-433.
  16. [IOk] R. Ishimura and Y. Okada, Sur la condition (S) de Kawai et la propriété de croissance régulière d'une fonction sous-harmonique et d'une fonction entière, Kyushu J. Math. 48 (1994), 257-263.
  17. [Kan] A. Kaneko, Introduction to Hyperfunctions, Kluwer Acad. Publ., 1988.
  18. [KS] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss. 292, Springer, 1990.
  19. [Kaw] T. Kawai, On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 17 (1970), 467-517.
  20. [Ki] C. O. Kiselman, Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants, Bull. Soc. Math. France 97 (1969), 329-356.
  21. [Ko1] Yu. F. Korobeĭnik, On solutions of some functional equations in classes of functions analytic in convex domains, Mat. Sb. 75 (1968), 225-234 (in Russian); English transl.: Math. USSR-Sb. 4 (1968), 203-211.
  22. [Ko2] Yu. F. Korobeĭnik, The existence of an analytic solution of an infinite order differential equation and the nature of its domain of analyticity, Mat. Sb. 80 (1969), 52-76 (in Russian); English transl.: Math. USSR-Sb. 9 (1969), 53-71.
  23. [Ko3] Yu. F. Korobeĭnik, Convolution equations in the complex domain, Mat. Sb. 127 (1699 (1985) (in Russian); English transl.: Math. USSR-Sb. 55 (1985), 171-193.
  24. [LG] P. Lelong and L. Gruman, Entire Functions of Several Complex Variables, Grundlehren Math. 282, Springer, 1986.
  25. [L] B. Ja. Levin, Distribution of Zeros of Entire Functions, Trans. Math. Monographs 5, Amer. Math. Soc., 1964.
  26. [M] B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble) 6 (1955-1956), 271-354.
  27. [MéSt] A. Méril and D. C. Struppa, Convolutors in spaces of holomorphic functions, in: Lecture Notes in Math. 1276, Springer, 1987, 253-275.
  28. [Mo1] V. V. Morzhakov, Convolution equations in spaces of functions holomorphic in convex domains and on convex compacta in ℂn, Mat. Zametki 16 (1974), 431-440 (in Russian); English transl.: Math. Notes 16 (1974), 846-851.
  29. [Mo2] V. V. Morzhakov, On epimorphicity of a convolution operator in a convex domains in ℂl, Mat. Sb. 132 (174) (1987), 352-370 (in Russian); Math. USSR-Sb. 60 (1988), 347-364.
  30. [Mo3] V. V. Morzhakov, Convolution equations in convex domains of ℂn, in: Complex Anal. and Appl. '87, Sofia, 1989, 360-364.
  31. [N] V. V. Napalkov, Convolution equations in multidimensional spaces, Mat. Zametki 25 (1979), 761-774 (in Russian); English transl.: Math. Notes 25 (1979).
  32. [O] Y. Okada, Stability of convolution operators, Publ. RIMS Kyoto Univ., to appear.
  33. [Sé] A. Sébbar, Prolongement des solutions holomorphes de certains opérateurs différentiels d'ordre infini à coefficients constants, in: Sém. Lelong-Skoda, Lecture Notes in Math. 822, Springer, 1980, 199-220.
  34. [T] V. A. Tkachenko, Equations of convolution type in spaces of analytic functionals, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 378-392 (in Russian); English transl.: Math. USSR-Izv. 11 (1977), 361-374.
  35. [V] A. Vidras, Interpolation and division problems in spaces of entire functions with growth conditions and their applications, Doct. Diss., Univ. of Maryland, 1992.
  36. [Z] M. Zerner, Domaines d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris 272 (1971), 1646-1648.
Banach Center Publications
1996/33/1
Export to PBN, Opens in new tab
Pages:
105-114
Main language of publication
English
Published
1996
Exact and natural sciences