On continuation of real analytic solutions of linear partial differential equations
Analytic solutions of partial differential equations - Trento, 1981, Astérisque, no. 89-90 (1981), pp. 11-44

Voir la notice du chapitre de livre provenant de la source Numdam

MR Zbl
Kaneko, A. On continuation of real analytic solutions of linear partial differential equations, dans Analytic solutions of partial differential equations - Trento, 1981, Astérisque, no. 89-90 (1981), pp. 11-44. http://geodesic.mathdoc.fr/item/AST_1981__89-90__11_0/
@incollection{AST_1981__89-90__11_0,
     author = {Kaneko, A.},
     title = {On continuation of real analytic solutions of linear partial differential equations},
     booktitle = {Analytic solutions of partial differential equations - Trento, 1981},
     series = {Ast\'erisque},
     pages = {11--44},
     year = {1981},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {89-90},
     mrnumber = {666402},
     zbl = {0518.35007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AST_1981__89-90__11_0/}
}
TY  - CHAP
AU  - Kaneko, A.
TI  - On continuation of real analytic solutions of linear partial differential equations
BT  - Analytic solutions of partial differential equations - Trento, 1981
AU  - Collectif
T3  - Astérisque
PY  - 1981
SP  - 11
EP  - 44
IS  - 89-90
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/AST_1981__89-90__11_0/
LA  - en
ID  - AST_1981__89-90__11_0
ER  - 
%0 Book Section
%A Kaneko, A.
%T On continuation of real analytic solutions of linear partial differential equations
%B Analytic solutions of partial differential equations - Trento, 1981
%A Collectif
%S Astérisque
%D 1981
%P 11-44
%N 89-90
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/AST_1981__89-90__11_0/
%G en
%F AST_1981__89-90__11_0

S. Bochner [1] Partial differential equations and analytic continuation, Proc. Nat Acad. Sci. 38 (1952), 227-230. | MR | Zbl | DOI

J. M. Bony [1] Propagation des singularités différentiables pour des opérateurs à coefficients analytiques, Astérisque 34-35 (1976), 43-91. | Zbl | EuDML | MR

C. C. Chou [1] La Transformation de Fourier Complexe et l'Equation de Convolution, Lecture Notes in Math. 325, Springer, (1973). | MR | Zbl

L. Ehrenpreis [1] A new proof and an extension of Hartogs' theorem, Bull. Amer. Math. Soc. 67 (1961), 507-509. | MR | Zbl | DOI

L. Ehrenpreis [2] Fourier Analysis in Several Complex Variables, J. Wiley-Inter-science, 1970. | MR | Zbl

V. V. Grušin [1]On solutions with isolated singularities for partial differential equations with constant coefficients, Trudy Moskov. Mat. Obšč. 15 (1966), 262-278 (in Russian). | MR | Zbl

F. Hartogs [1] Einige Folgerungen aus der Cauchyschen Integralformel bei Funktionen mehrer Veränderlichen, Sitzb. Münchener Acad. 36 (1906), 223. | JFM

A. Kaneko [1] On continuation of regular solutions of partial differential equations to compact convex sets, J. Fac. Sei. Univ. Tokyo, Sec. IA, 17 (1970), 567-580. | MR | Zbl

A. Kaneko [2] On continuation of regular solutions of partial differential equations to compact convex sets II, ibid. 18 (1971), 415-433. | Zbl

A. Kaneko [3] Fundamental Principle and extension of solutions of linear partial differential equations with constant coefficients. Lecture Notes in Math. 287, Springer, (1973), 122-134. | MR | Zbl

A. Kaneko [4] On continuation of regular solutions of partial differential equations with constant coefficients, J. Math. Soc. Japan 26 (1974), 92-123. | Zbl | MR | DOI

A. Kaneko [5] Remarks on hyperfunctions with analytic parameters, J. Fac. Sci. Univ. Tokyo, Sec. IA 22 (1975), 371-407. | MR | Zbl

A. Kaneko [6] Remarks on hyperfunctions with analytic parameters II, ibid. 25 (1978), 67-73. | MR | Zbl

Α. Kaneko [7] On continuation of regular solutions of linear partial differential equations with real analytic coefficients, Proc. Japan Acad. 51 (1975), Suppl. 798-801. | MR | Zbl | DOI

Α. Kaneko [8] Singular spectrum of boundary values of solutions of partial differential equations with real analytic coefficients. Sci. Pap. Col. Gen. Educ. Univ. Tokyo 25 (1975), 59-68 ; Correction in [12], Appendix B. | Zbl | MR

Α. Kaneko [9] On continuation of regular solutions of linear partial differential equations, Publ. RIMS Kyoto Univ. 12, Suppl. (1977), 113-121. | Zbl | MR | DOI

Α. Kaneko [10] Prolongement des solutions régulières de l'équation aux dérivées partielles a coefficients constants. Séminaire Goulaouic-Schwartz 1976-77, Exposé no 18. | MR | Zbl | Numdam

Α. Kaneko [11] Introduction a la théorie des hyperfonctions I, II, Cours de DEA, Univ. de Grenoble, (1977-78). Revised edition in Japanese : Chôkansû-Nyûmon, part. I, Univ. of Tokyo Press, 1980.

Α. Kaneko [12] Estimation of singular spectrum of boundary values for some semi-hyperbolic operators, J. Fac. Sci. Univ. Tokyo Sec. IA 27 (1980), 401-461. | MR | Zbl

Α. Kaneko [13] On the propagation of micro-analyticity along the boundary, submitted to J. Fac. Sci. Univ. Tokyo, Sec. IA. | MR | Zbl

M. Kashiwara and T. Kawai [1] On the boundary value problem for elliptic system of linear differential equations II, Proc. Japan Acad. 49 (1973), 164-168. | MR | Zbl | DOI

K. Kataoka [1] On the theory of Radon transformations of hyperfunctions, J. Fac. Sci. Univ. Tokyo Sec. IA (to appear). | MR | Zbl

K. Kataoka [2] Micro-local theory of boundary value problems I. Theory of mild hyperfunctions and Green's formula, J. Fac. Sci. Univ. Tokyo, Sec. IA 27 (1980), 355-399. | MR | Zbl

K. Kataoka [3] Micro-local theory of boundary value problems II. Theorems on regularity up to the boundary for reflective and diffractive operators, ibid. 28 (1981), 31-56. | Zbl | MR

T. Kawai [1] On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo Sec. IA 17 (1970), 467-517. | Zbl | MR

T. Kawai [2] Construction of local elementary solutions for linear partial differential operators with real analytic coefficients I, Publ. RIMS Kyoto Univ. 17 (1971), 363-397. | MR | Zbl | DOI

H. Komatsu [1] Relative cohomology of sheaves of solutions of differential equations. Séminaire Lions-Schwartz 1966-67. Reprint: Lecture Notes in Math. 287, Springer, 1973, pp. 192-261. | Zbl | MR

H. Komatsu [2] A local version of Bochner's tube theorem, J. Fac. Sci. Univ. Tokyo Sec. IA 19 (1972), 201-214. | MR | Zbl

H. Komatsu and T. Kawai [1] Boundary values of hyperfunction solutions of linear partial differential equations, Publ. RIMS Kyoto Univ. 7 (1971), 95-104. | MR | Zbl | DOI

B. Malgrange [l] Sur les systèmes différentiels à coefficients constants, Séminaire Leray, 1961-62. | EuDML | Zbl

M. Morimoto [1] Edge of the wedge theorem and hyperfunction. Lecture Notes in Math. 287, Springer, 1971, pp. 41-81. | Zbl | MR

V. P. Palamodov [1] Linear differential equations with constant coefficients, Moskva, (1967), (in Russian). English translation: Springer, 1970 ; Japanese translation: Yoshioka, 1972-73. | MR | Zbl

B. Riemann [1] Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse, Gesam. Math. Werke, pp. 3-48.

M. Sato, T. Kawai and M. Kashiwara (S-K-K) [1] Microfunctions and pseudo-differential equations, Lecture Notes in Math. 287, Springer 1973, pp. 263-529. | MR | Zbl

P. Schapira [1] Problème de Dirichlet et solutions des hyperfonctions des équations elliptiques, Bull. UMI (4), 3 (1969), 367-372. | MR | Zbl

P. Schapira [2] Propagation at the boundary and reflection of analytic singularities of solutions of linear partial differential equations I, Publ. RIMS Kyoto Univ. 12 Suppl. (1977), 441-453. | MR | Zbl | DOI

P. Schapira [3] Propagation au bord et reflexion des singularités analytiques des solutions des équations aux dérivées partielles II, Séminaire Goulaouic-Schwartz 1976-77, Exposé n. 9. | Zbl | EuDML | MR | Numdam

J. Sjöstrand [1] Sur la propagation des singularités analytiques pour certains problèmes de Dirichlet, C. R. Acad. Sc. Paris 288 (1979), 673-674. | MR | Zbl