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1992 | 27 | 1 | 183-195
Tytuł artykułu

On continuation of regular solutions of linear partial differential equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
27
Numer
1
Strony
183-195
Opis fizyczny
Daty
wydano
1992
Twórcy
autor
  • Department of Mathematics, College of General Education, University of Tokyo, Tokyo, Japan
Bibliografia
  • W. Abramczuk, On continuation of quasi-analytic solutions of partial differential equations to compact convex sets, J. Austral. Math. Soc. 39 (1985), 306-316.
  • Sh. A. Akhmedov, On continuation of generalized solutions of differential equations defined on a neighborhood of characteristic subspaces, Dokl. Akad. Nauk SSSR 197 (1971), 255-256.
  • A. Andreotti, Complexes of Partial Differential Operators, Yale University, 1975.
  • 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.
  • G. Bengel, Sur le prolongement analytique des solutions d'une équation aux dérivées partielles, C. R. Acad. Sci. Paris 273 (1971), 572-574.
  • J. Bochner, Partial differential equations and analytic continuation, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 227-230.
  • J. M. Bony et P. Schapira, Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, Invent. Math. 17 (1972), 95-105.
  • J. M. Bony et P. Schapira, Solutions hyperfonctions du problème de Cauchy, in: Lecture Notes in Math. 287, Springer, 1973, 82-98.
  • L. A. Chudov, On singularities of solutions of linear partial differential equations with constant coefficients, Dokl. Akad. Nauk SSSR 125 (1959), 504-507 (in Russian).
  • L. Ehrenpreis, A new proof and extension of Hartogs' theorem, Bull. Amer. Math. Soc. 67 (1961), 507-509.
  • L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Wiley-Interscience, 1970.
  • R. Finn, Isolated singularities of solutions of non-linear partial differential equations, Trans. Amer. Math. Soc. 75 (1953), 385-403.
  • E. A. Gorin and V. V. Grushin, On some local theorem for partial differential equations with constant coefficients, Trudy Moskov. Mat. Obshch. 14 (1965), 200-210 (in Russian).
  • V. V. Grushin, On the Q-hypoelliptic equations, Mat. Sb. 57 (1962), 233-240 (in Russian).
  • >V. V. Grushin, On solutions with isolated singularities for partial differential equations with constant coefficients, Trudy Moskov. Mat. Obshch. 15 (1966), 262-278 (in Russian).
  • F. Hartogs, Einige Folgerungen aus der Cauchyschen Integralformel bei Funktionen mehrerer Veränderlichen, Sitzb. Münchener Acad. 36 (1906), 223-241.
  • F. Hartogs, Über die aus den singulären Stellen einer analytischen Funktion mehrerer Veränderlichen bestehenden Gebilde, Acta Math. 32 (1908), 57-79.
  • R. Harvey and J. Polking, Removable singularities of solutions of linear partial differential equations, ibid. 125 (1970), 39-56.
  • L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-182.
  • F. John, Plane Waves and Spherical Means, Interscience, 1955.
  • A. Kaneko, On continuation of regular solutions of partial differential equations to compact convex sets, J. Fac. Sci. Univ. Tokyo Sect. 1A 17 (1970), 567-580; II, ibid. 18 (1972), 415-433.
  • A. Kaneko, On continuation of regular solutions of partial differential equations with constant coefficients, J. Math. Soc. Japan 26 (1974), 92-123.
  • A. Kaneko, Note on continuation of real analytic solutions of partial differential equations with constant coefficients, Proc. Japan Acad. 51 (1975), 262-264.
  • A. Kaneko, Singular spectrum of boundary values of solutions of partial differential equations with real analytic coefficients, Sci. Pap. Coll. Gen. Educ. Univ. Tokyo 25 (1975), 59-68.
  • A. Kaneko, On continuation of regular solutions of linear partial differential equations, Publ. RIMS Kyoto Univ. 12 Suppl. (1977), 113-121.
  • A. Kaneko, Prolongement des solutions régulières de l'équation aux dérivées partielles à coefficients constants, Séminaire Goulaouic-Schwartz, 1976/7, Exposé no 18.
  • A. Kaneko, Estimation of singular spectrum of boundary values for some semi-hyperbolic operators, J. Fac. Sci. Univ. Tokyo Sec. 1A 27 (1980), 401-461.
  • A. Kaneko, On continuation of real analytic solutions of linear partial differential equations, Astérisque 89-90 (1981), 11-44.
  • A. Kaneko, On the propagation of micro-analyticity along the boundary, J. Fac. Sci. Univ. Tokyo Sect. 1A 29 (1982), 319-352.
  • A. Kaneko, Continuation of real analytic solutions to convex conical singularities, Sûrikaisekikenkyûsho Kôkyûroku 592 (1986), 149-172 (in Japanese).
  • A. Kaneko, On the analyticity of the locus of singularity of real analytic solutions with minimal dimension, Nagoya Math. J. 104 (1986), 63-84.
  • A. Kaneko, Nishino-Yamaguchi theory and its application to the theory hyperfunctions, in: Proc. 7th Daewoo Workshop on Pure Math., Seoul, 1987, 241-261.
  • A. Kaneko, On Hartogs type continuation theorem for regular solutions of linear partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo 35 (1988), 1-26.
  • A. Kaneko, Hartogs type extension theorem of real analytic solutions of linear partial differential equations with constant coefficients, in: Advances in the Theory of Fréchet Spaces, Kluwer, 1989, 63-72.
  • A. Kaneko, Introduction to Hyperfunctions, Kluwer, Tokyo 1988.
  • A. Kaneko, Analyticité du lieu de singularité de dimension minimale d'une solution analytique réelle, in: Geometrical and Algebraical Aspects in Several Complex Variables, Editel, Rende, 1991, 155-167.
  • K. Kataoka, Micro-local theory of boundary value problems II, J. Fac. Sci. Univ. Tokyo Sect. 1A 28 (1981), 31-56.
  • T. Kawai, On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, ibid. 17 (1970), 467-517.
  • T. Kawai, Removable singularities of solutions of systems of linear differential equations, Bull. Amer. Math. Soc. 81 (1975), 461-463.
  • T. Kawai, Extension of solutions of systems of linear differential equations, Publ. RIMS Kyoto Univ. 12 (1976), 215-227.
  • T. Kawai, A differential equation theoretic interpretation of a geometric result of Hartogs, Proc. Amer. Math. Soc. 98 (1986), 222-224.
  • C. O. Kiselman, Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants, Bull. Soc. Math. France 97 (1969), 329-356.
  • H. Komatsu, Relative cohomology of sheaves of solutions of differential equations, Séminaire Lions-Schwartz, 1966-67 (reprinted in: Lecture Notes in Math. 287, Springer, 1973, 192-261).
  • H. Komatsu and T. Kawai, Boundary values of hyperfunction solutions of linear partial differential equations, Publ. RIMS Kyoto Univ. 7 (1971), 95-104.
  • W. Littman, Polar sets and removable singularities of partial differential equations, Ark. Mat. 7 (1967), 1-9.
  • B. Malgrange, Sur la propagation de la régularité des solutions des équations à coefficients constants, Bull. Math. Soc. Roumanie 3 (1959), 433-440.
  • B. Malgrange, Sur les systèmes différentiels à coefficients constants, Séminaire Leray, 1961-62.
  • A. Meril et D. C. Struppa, Phénomène de Hartogs et équations de convolution, Séminaire Lelong-Skoda, 1985-86, Lecture Notes in Math. 1295, Springer, 146-156.
  • T. Ôaku, Boundary value problems for systems of linear partial differential equations and propagation of micro-analyticity, J. Fac. Sci. Univ. Tokyo Sect. 1A 33 (1986), 175-232.
  • T. Ôaku, Removable singularities of solutions of linear partial differential equations--systems and Fuchsian equations, ibid., 403-428.
  • K. Oka, Note sur les familles de fonctions analytiques multiformes etc., J. Hiroshima Univ. 4 (1934), 93-98.
  • V. P. Palamodov, Linear Differential Equations with Constant Coefficients, Nauka, Moscow 1967 (in Russian; English translation 1970 from Springer; Japanese translation 1972-73 from Yoshioka, Kyoto).
  • Ph. Pallu de la Barrière, Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, C. R. Acad. Sci. Paris 279 (1974), 947-949.
  • J. Presson, Local analytic continuation of holomorphic solutions of partial differential equations, Ann. Mat. Pura Appl. 112 (1977), 193-204.
  • J. Presson, On the analytic continuation of holomorphic solutions of partial differential equations, Ark. Mat. 19 (1981), 177-191.
  • J. C. Polking, A survey of removable singularities, in: Seminar on Non-linear Partial Differential Equations, S. S. Chern (ed.), Springer, 1984, 261-292.
  • B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse, Gesam. Math. Werke, 3-48.
  • A. Sadullaev and E. M. Chirka, On continuation of functions with polar singularities, Mat. Sb. 132 (1987), 383-390.
  • P. Schapira, Propagation au bord et reflexion des singularités analytiques des équations aux dérivées partielles II, Séminaire Goulaouic-Schwartz 1976-77, exposé no. 9.
  • P. Schapira, Propagation at the boundary of analytic singularities, in: Proceedings NATO Symposium Maratea, Reidel, 1980, 185-212.
  • P. Schapira, Propagation of analytic singularities up to non smooth boundaries, in: Colloque E.D.P. Saint-Jean de Monts, 1987.
  • F. Severi, Una proprietà fondamentale dei campi di olomorfismo di una funzione analitica di una variabile reale e di una variabile complessa, Rend. R. Accad. Lincei 15 (1932), 487-490.
  • D. Struppa, The first eighty years of Hartogs theorem, in: Seminari di Geometria 1987-88, Univ. di Bologna, 127-209.
  • S. Tajima, Analyse microlocale sur les variétés de Cauchy-Riemann et le problème du prolongement des solutions holomorphes des équations aux dérivées partielles, Publ. RIMS Kyoto Univ. 18 (1982), 911-945.
  • Y. Tsuno, On the prolongation of local holomorphic solutions of partial differential equations, J. Math. Soc. Japan 26 (1974), 523-548.
  • Y. Tsuno, On the prolongation of local holomorphic solutions of non-linear partial differential equations, ibid. 27 (1975), 454-466.
  • Y. Tsuno, Analytic continuation of holomorphic solutions of partial differential equations, Sûrikaiseki-Kenkyûsho Kôkyûroku 281 (1976), 120-162 (in Japanese).
  • M. Uchida, Continuation of analytic solutions to linear partial differential equations up to convex conical singularities, preprint.
  • M. Uchida and G. Zampieri, Second microlocalization at the boundary and microhyperbolicity, Publ. RIMS Kyoto Univ. 26 (1990), 205-219.
  • G. Zampieri, Propagation of microanalyticity at the boundary for solutions of linear differential equations, J. Fac. Sci. Univ. Tokyo Sect. 1A 33 (1986), 429-439.
  • M. Zerner, Domaine d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris 272 (1971), 1646-1648.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv27z1p183bwm
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