@article{bwmeta1.element.bwnjournal-article-bcpv27z1p183bwm,
author = {Kaneko, Akira},
title = {On continuation of regular solutions of linear partial differential equations},
journal = {Banach Center Publications},
volume = {27},
year = {1992},
pages = {183-195},
zbl = {0791.35016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z1p183bwm}
}
Kaneko, Akira. On continuation of regular solutions of linear partial differential equations. Banach Center Publications, Tome 27 (1992) pp. 183-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z1p183bwm/
[000] W. Abramczuk, On continuation of quasi-analytic solutions of partial differential equations to compact convex sets, J. Austral. Math. Soc. 39 (1985), 306-316. | Zbl 0595.35015
[001] 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.
[002] A. Andreotti, Complexes of Partial Differential Operators, Yale University, 1975. | Zbl 0309.58020
[003] 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. | Zbl 0344.35065
[004] G. Bengel, Sur le prolongement analytique des solutions d'une équation aux dérivées partielles, C. R. Acad. Sci. Paris 273 (1971), 572-574. | Zbl 0217.41001
[005] J. Bochner, Partial differential equations and analytic continuation, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 227-230. | Zbl 0046.09902
[006] J. M. Bony et P. Schapira, Existence et prolongement des solutions holomorphes des équations aux dérivées partielles, Invent. Math. 17 (1972), 95-105. | Zbl 0225.35008
[007] J. M. Bony et P. Schapira, Solutions hyperfonctions du problème de Cauchy, in: Lecture Notes in Math. 287, Springer, 1973, 82-98.
[008] 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). | Zbl 0089.07302
[009] L. Ehrenpreis, A new proof and extension of Hartogs' theorem, Bull. Amer. Math. Soc. 67 (1961), 507-509. | Zbl 0099.07801
[010] L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Wiley-Interscience, 1970. | Zbl 0195.10401
[011] R. Finn, Isolated singularities of solutions of non-linear partial differential equations, Trans. Amer. Math. Soc. 75 (1953), 385-403. | Zbl 0053.39205
[012] 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). | Zbl 0162.14702
[013] V. V. Grushin, On the Q-hypoelliptic equations, Mat. Sb. 57 (1962), 233-240 (in Russian). | Zbl 0104.07302
[014] >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).
[015] F. Hartogs, Einige Folgerungen aus der Cauchyschen Integralformel bei Funktionen mehrerer Veränderlichen, Sitzb. Münchener Acad. 36 (1906), 223-241. | Zbl 37.0443.01
[016] F. Hartogs, Über die aus den singulären Stellen einer analytischen Funktion mehrerer Veränderlichen bestehenden Gebilde, Acta Math. 32 (1908), 57-79. | Zbl 40.0472.01
[017] R. Harvey and J. Polking, Removable singularities of solutions of linear partial differential equations, ibid. 125 (1970), 39-56. | Zbl 0214.10001
[018] L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-182. | Zbl 0282.35015
[019] F. John, Plane Waves and Spherical Means, Interscience, 1955. | Zbl 0067.32101
[020] 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.
[021] A. Kaneko, On continuation of regular solutions of partial differential equations with constant coefficients, J. Math. Soc. Japan 26 (1974), 92-123. | Zbl 0265.35010
[022] A. Kaneko, Note on continuation of real analytic solutions of partial differential equations with constant coefficients, Proc. Japan Acad. 51 (1975), 262-264. | Zbl 0319.35015
[023] 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. | Zbl 0332.35048
[024] A. Kaneko, On continuation of regular solutions of linear partial differential equations, Publ. RIMS Kyoto Univ. 12 Suppl. (1977), 113-121. | Zbl 0369.35009
[025] A. Kaneko, Prolongement des solutions régulières de l'équation aux dérivées partielles à coefficients constants, Séminaire Goulaouic-Schwartz, 1976/7, Exposé no 18.
[026] 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.
[027] A. Kaneko, On continuation of real analytic solutions of linear partial differential equations, Astérisque 89-90 (1981), 11-44.
[028] A. Kaneko, On the propagation of micro-analyticity along the boundary, J. Fac. Sci. Univ. Tokyo Sect. 1A 29 (1982), 319-352. | Zbl 0497.35019
[029] A. Kaneko, Continuation of real analytic solutions to convex conical singularities, Sûrikaisekikenkyûsho Kôkyûroku 592 (1986), 149-172 (in Japanese).
[030] A. Kaneko, On the analyticity of the locus of singularity of real analytic solutions with minimal dimension, Nagoya Math. J. 104 (1986), 63-84. | Zbl 0595.35007
[031] A. Kaneko, Nishino-Yamaguchi theory and its application to the theory hyperfunctions, in: Proc. 7th Daewoo Workshop on Pure Math., Seoul, 1987, 241-261.
[032] 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. | Zbl 0654.35013
[033] 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.
[034] A. Kaneko, Introduction to Hyperfunctions, Kluwer, Tokyo 1988. | Zbl 0687.46027
[035] 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.
[036] K. Kataoka, Micro-local theory of boundary value problems II, J. Fac. Sci. Univ. Tokyo Sect. 1A 28 (1981), 31-56.
[037] T. Kawai, On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, ibid. 17 (1970), 467-517. | Zbl 0212.46101
[038] T. Kawai, Removable singularities of solutions of systems of linear differential equations, Bull. Amer. Math. Soc. 81 (1975), 461-463. | Zbl 0298.35043
[039] T. Kawai, Extension of solutions of systems of linear differential equations, Publ. RIMS Kyoto Univ. 12 (1976), 215-227. | Zbl 0366.58013
[040] T. Kawai, A differential equation theoretic interpretation of a geometric result of Hartogs, Proc. Amer. Math. Soc. 98 (1986), 222-224. | Zbl 0605.32004
[041] C. O. Kiselman, Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants, Bull. Soc. Math. France 97 (1969), 329-356. | Zbl 0189.40502
[042] 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).
[043] H. Komatsu and T. Kawai, Boundary values of hyperfunction solutions of linear partial differential equations, Publ. RIMS Kyoto Univ. 7 (1971), 95-104. | Zbl 0225.35032
[044] W. Littman, Polar sets and removable singularities of partial differential equations, Ark. Mat. 7 (1967), 1-9. | Zbl 0158.11004
[045] B. Malgrange, Sur la propagation de la régularité des solutions des équations à coefficients constants, Bull. Math. Soc. Roumanie 3 (1959), 433-440. | Zbl 0109.32002
[046] B. Malgrange, Sur les systèmes différentiels à coefficients constants, Séminaire Leray, 1961-62.
[047] 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.
[048] 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. | Zbl 0626.35058
[049] T. Ôaku, Removable singularities of solutions of linear partial differential equations--systems and Fuchsian equations, ibid., 403-428. | Zbl 0626.35011
[050] K. Oka, Note sur les familles de fonctions analytiques multiformes etc., J. Hiroshima Univ. 4 (1934), 93-98. | Zbl 60.0243.06
[051] 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).
[052] 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. | Zbl 0289.35004
[053] J. Presson, Local analytic continuation of holomorphic solutions of partial differential equations, Ann. Mat. Pura Appl. 112 (1977), 193-204.
[054] J. Presson, On the analytic continuation of holomorphic solutions of partial differential equations, Ark. Mat. 19 (1981), 177-191.
[055] J. C. Polking, A survey of removable singularities, in: Seminar on Non-linear Partial Differential Equations, S. S. Chern (ed.), Springer, 1984, 261-292.
[056] B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse, Gesam. Math. Werke, 3-48.
[057] A. Sadullaev and E. M. Chirka, On continuation of functions with polar singularities, Mat. Sb. 132 (1987), 383-390. | Zbl 0617.32018
[058] P. Schapira, Propagation au bord et reflexion des singularités analytiques des équations aux dérivées partielles II, Séminaire Goulaouic-Schwartz 1976-77, exposé no. 9. | Zbl 0361.35062
[059] P. Schapira, Propagation at the boundary of analytic singularities, in: Proceedings NATO Symposium Maratea, Reidel, 1980, 185-212.
[060] P. Schapira, Propagation of analytic singularities up to non smooth boundaries, in: Colloque E.D.P. Saint-Jean de Monts, 1987. | Zbl 0666.58043
[061] 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.
[062] D. Struppa, The first eighty years of Hartogs theorem, in: Seminari di Geometria 1987-88, Univ. di Bologna, 127-209. | Zbl 0657.35018
[063] 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. | Zbl 0553.58028
[064] Y. Tsuno, On the prolongation of local holomorphic solutions of partial differential equations, J. Math. Soc. Japan 26 (1974), 523-548. | Zbl 0279.35012
[065] Y. Tsuno, On the prolongation of local holomorphic solutions of non-linear partial differential equations, ibid. 27 (1975), 454-466. | Zbl 0303.35011
[066] Y. Tsuno, Analytic continuation of holomorphic solutions of partial differential equations, Sûrikaiseki-Kenkyûsho Kôkyûroku 281 (1976), 120-162 (in Japanese).
[067] M. Uchida, Continuation of analytic solutions to linear partial differential equations up to convex conical singularities, preprint. | Zbl 0791.35005
[068] M. Uchida and G. Zampieri, Second microlocalization at the boundary and microhyperbolicity, Publ. RIMS Kyoto Univ. 26 (1990), 205-219. | Zbl 0712.35007
[069] 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. | Zbl 0651.35005
[070] M. Zerner, Domaine d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris 272 (1971), 1646-1648. | Zbl 0213.37004