no. 3
Harmonic synthesis of solutions of elliptic equation with periodic coefficients
Annales de l'Institut Fourier, Volume 43 (1993) no. 3, pp. 751-768

An elliptic system in ℝ n , which is invariant under the action of the group ℤ n is considered. We construct a holomorphic family of finite-dimensional subrepresentations of the group in the space of solutions (Floquet solutions), such that any solution of the growth O( exp (a|x|)) at infinity can be rewritten in the form of an integral over the family.

On consière un système dans ℝ n de type elliptique admettant le groupe d’invariance ℤ n . Nous construisons une famille holomorphe de sous-représentations de ce groupe dans l’espace des solutions (de Floquet) telle que chaque solution qui est égale à O( exp (a|x|)) à l’infini, peut être représentée sous la forme d’une intégrale dans cette famille.

Palamodov, Victor P. Harmonic synthesis of solutions of elliptic equation with periodic coefficients. Annales de l'Institut Fourier, Volume 43 (1993) no. 3, pp. 751-768. doi: 10.5802/aif.1354
@article{AIF_1993__43_3_751_0,
     author = {Palamodov, Victor P.},
     title = {Harmonic synthesis of solutions of elliptic equation with periodic coefficients},
     journal = {Annales de l'Institut Fourier},
     pages = {751--768},
     year = {1993},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {3},
     doi = {10.5802/aif.1354},
     zbl = {0784.35023},
     mrnumber = {95f:35037},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1354/}
}
TY  - JOUR
AU  - Palamodov, Victor P.
TI  - Harmonic synthesis of solutions of elliptic equation with periodic coefficients
JO  - Annales de l'Institut Fourier
PY  - 1993
SP  - 751
EP  - 768
VL  - 43
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1354/
DO  - 10.5802/aif.1354
LA  - en
ID  - AIF_1993__43_3_751_0
ER  - 
%0 Journal Article
%A Palamodov, Victor P.
%T Harmonic synthesis of solutions of elliptic equation with periodic coefficients
%J Annales de l'Institut Fourier
%D 1993
%P 751-768
%V 43
%N 3
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1354/
%R 10.5802/aif.1354
%G en
%F AIF_1993__43_3_751_0

[1] V.P. Palamodov, Linear differential operators with constant coefficients, Moscow, Nauka, 1967, Springer-Verlag, 1970. | Zbl

[2] L. Ehrenpreis, Fourier analysis in several complex variables, N.Y., 1970. | Zbl | MR

[3] I.M. Gel'Fand, Eigenfunction decomposition of equation with periodic coefficients, Doklady ANSSSR, 73, n° 6 (1950), 1117-1120 (Russian).

[4] P.A. Kuchment, Floquet theory for partial differential equations, Russian Math. Surveys, 37, n° 4 (1982), 1-50. | Zbl | MR

[5] L. Bungart, On analytic fibre bundles I. Holomorphic fiber bundles with infinite dimensional fibres, Topology, 7 (1968), 55-68. | Zbl | MR

[6] V.P. Palamodov, The projective limit on the category of linear topological spaces, Mathematics of the USSR Sbornik, 4 (1968), 529-559. | Zbl

[7] O. Zariski, P. Samuel, Commutative algebra, Ch. IV, Van Nostrand, 1958.

[8] N. Bourbaki, L'algèbre commutative, Paris, Hermann, 1967.

[9] V.P. Palamodov, Differential operators in coherent analytic sheaves, Mathematics of the USSR Sbornik, 6 (1968), 365-391. | Zbl | MR

[10] Y.T. Siu, Noether-Lasker decomposition of coherent analytic subsheaves, Trans. of A.M.S., 135 (1969), 375-385. | Zbl | MR

[11] R. Gunning, H. Rossi, Analytic functions of serveral complex variables, Englewood Cliffs, Prentice Hall, 1965. | Zbl | MR

[12] B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations des convolution, Ann. Inst. Fourier, Grenoble, 6 (1955-1956), 271-355. | Zbl | Numdam | MR | EuDML

[13] V.P. Palamodov, Deformation of complex spaces, Russian Math. Surveys, 31 (1976), 129-197. | Zbl | MR

Cited by Sources: