Harmonic synthesis of solutions of elliptic equation with periodic coefficients
Palamodov, Victor P.
Annales de l'Institut Fourier, Tome 43 (1993), p. 751-768 / Harvested from Numdam
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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.

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.

@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},
     volume = {43},
     year = {1993},
     pages = {751-768},
     doi = {10.5802/aif.1354},
     mrnumber = {95f:35037},
     zbl = {0784.35023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1993__43_3_751_0}
}

Palamodov, Victor P. Harmonic synthesis of solutions of elliptic equation with periodic coefficients. Annales de l'Institut Fourier, Tome 43 (1993) pp. 751-768. doi : 10.5802/aif.1354. http://gdmltest.u-ga.fr/item/AIF_1993__43_3_751_0/

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