An elementary theory of hyperfunctions and microfunctions

Hikosaburo Komatsu

Banach Center Publications (1992)

  • Volume: 27, Issue: 1, page 233-256
  • ISSN: 0137-6934

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Komatsu, Hikosaburo. "An elementary theory of hyperfunctions and microfunctions." Banach Center Publications 27.1 (1992): 233-256. <http://eudml.org/doc/262741>.

@article{Komatsu1992,
author = {Komatsu, Hikosaburo},
journal = {Banach Center Publications},
keywords = {microfunctions; ultradistributions},
language = {eng},
number = {1},
pages = {233-256},
title = {An elementary theory of hyperfunctions and microfunctions},
url = {http://eudml.org/doc/262741},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Komatsu, Hikosaburo
TI - An elementary theory of hyperfunctions and microfunctions
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 1
SP - 233
EP - 256
LA - eng
KW - microfunctions; ultradistributions
UR - http://eudml.org/doc/262741
ER -

References

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  1. [1] G. Bengel, Das Weylsche Lemma in der Theorie der Hyperfunktionen, Math. Z. 96 (1967), 373-392. 
  2. [2] G. Bengel et P. Schapira, Décomposition microlocale analytique des distributions, Ann. Inst. Fourier (Grenoble) 29 (3) (1979), 101-124. Zbl0396.46039
  3. [3] J.-M. Bony, Propagation des singularités différentiables pour une classe d'opérateurs différentiels à coefficients analytiques, Astérisque 34-35 (1976), 43-91. 
  4. [4] J.-M. Bony et P. Schapira, Propagation des singularités analytiques pour les solutions des équations aux dérivées partielles, Ann. Inst. Fourier (Grenoble) 26 (1) (1976), 81-140. Zbl0312.35064
  5. [5] J. W. de Roever, Hyperfunctional singular support of ultradistributions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), 585-631. Zbl0606.46027
  6. [6] J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), 183-269. Zbl0232.47055
  7. [7] L. Ehrenpreis, A fundamental principle for systems of linear differential equations with constant coefficients and some of its applications, in: Proc. Internat. Symp. on Linear Spaces, 1961, Jerusalem, 161-174. 
  8. [8] L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Wiley-Interscience, New York 1970. 
  9. [9] A. Eida, On microlocal decomposition of ultradistributions, Master's Thesis, Univ. Tokyo, 1989 (in Japanese). Zbl1008.58018
  10. [10] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. Zbl0108.07804
  11. [11] A. Grothendieck, Sur les espaces de solutions d'une classe générale d'équations aux dérivées partielles, J. Analyse Math. 2 (1952-53), 243-280. Zbl0051.08801
  12. [12] A. Grothendieck, Local Cohomology, Lecture Notes in Math. 41, Springer, Berlin 1967. 
  13. [13] R. Harvey, Hyperfunctions and linear partial differential equations, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 1042-1046. Zbl0138.36303
  14. [14] L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton 1966. Zbl0138.06203
  15. [15] L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), 79-183. Zbl0212.46601
  16. [16] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin 1983. Zbl0521.35001
  17. [17] A. Kaneko, Introduction to Hyperfunctions, Kluwer, Dordrecht 1988. Zbl0687.46027
  18. [18] M. Kashiwara, T. Kawai and T. Kimura, Foundations of Algebraic Analysis, Princeton Univ. Press, Princeton 1986. Zbl0605.35001
  19. [19] C. O. Kiselman, Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants, Bull. Soc. Math. France 97 (1969), 329-356. Zbl0189.40502
  20. [20] H. Komatsu, Resolutions by hyperfunctions of sheaves of solutions of differential equations with constant coefficients, Math. Ann. 176 (1968), 77-86. Zbl0161.29802
  21. [21] H. Komatsu, Boundary values for solutions of elliptic equations, in: Proc. Internat. Conf. on Functional Analysis and Related Topics, 1969, Univ. of Tokyo Press, 1970, 107-121. 
  22. [22] H. Komatsu, Relative cohomology of sheaves of solutions of differential equations, in: Lecture Notes in Math. 287, Springer, 1972, 192-259. 
  23. [23] H. Komatsu, Irregularity of characteristic elements and construction of null-solutions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), 297-342. Zbl0443.35009
  24. [24] H. Komatsu, Microlocal analysis in Gevrey classes and in complex domains, in: Microlocal Analysis and Applications, Lecture Notes in Math., 1495, Springer, 1991, 161-236. Zbl0791.35003
  25. [25] H. Komatsu and T. Kawai, Boundary values of hyperfunction solutions of linear partial differential equations, Publ. Res. Inst. Math. Sci. 7 (1971/72), 95-104. Zbl0225.35032
  26. [26] G. Köthe, Dualität in der Funktionentheorie, J. Reine Angew. Math. 191 (1953), 30-49. Zbl0050.33502
  27. [27] 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. 
  28. [28] B. Malgrange, Faisceaux sur des variétés analytiques réelles, Bull. Soc. Math. France 85 (1957), 231-237. Zbl0079.39201
  29. [29] F. Mantovani e S. Spagnolo, Functionali analitici reali e funzioni armoniche, Ann. Scuola Norm. Sup. Pisa (6) 18 (1964), 475-513. 
  30. [30] A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki 13, 1960-61, No. 214. 
  31. [31] A. Martineau, Le 'edge of the wedge theorem' en théorie des hyperfonctions de Sato, in: Proc. Internat. Conf. on Functional Analysis and Related Topics, 1969, Univ. of Tokyo Press, 1970, 95-106. 
  32. [32] M. Morimoto, Sur la décomposition du faisceau des germes de singularités d'hyperfonctions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 17 (1970), 215-239. Zbl0205.12904
  33. [33] C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. École Norm. Sup. 77 (1960), 41-121. Zbl0104.33403
  34. [34] M. Sato, On a generalization of the concept of functions, Proc. Japan Acad. 34 (1958), 126-130 & 604-608. Zbl0080.32303
  35. [35] M. Sato, Theory of hyperfunctions, I, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1959), 139-193. Zbl0087.31402
  36. [36] M. Sato, Theory of hyperfunctions, II, ibid. 8 (1960), 387-437. Zbl0097.31404
  37. [37] M. Sato, Hyperfunctions and partial differential equations, in: Proc. Internat. Conf. on Functional Analysis and Related Topics, 1969, Univ. of Tokyo Press, 1970, 91-94. 
  38. [38] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, in: Lecture Notes in Math. 287, Springer, 1973, 265-529. 
  39. [39] P. Schapira, Problème de Dirichlet et solutions hyperfonctions des équations elliptiques, Boll. Un. Mat. Ital. (4) 2 (1969), 367-372. Zbl0177.37101
  40. [40] L. Schwartz, Théorie des Distributions, Hermann, Paris 1950-51. 
  41. [41] J. Siciak, Holomorphic continuation of harmonic functions, Ann. Polon. Math. 29 (1974), 67-73. Zbl0247.32011
  42. [42] J. Sjöstrand, Singularités analytiques microlocales, Astérisque 95 (1982). Zbl0524.35007
  43. [43] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501

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