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

On consière un système dans ℝn de type elliptique admettant le groupe d’invariance ℤn. 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 ℝn, which is invariant under the action of the group ℤn 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.

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     author = {Palamodov, Victor P.},
     title = {Harmonic synthesis of solutions of elliptic equation with periodic coefficients},
     journal = {Annales de l'Institut Fourier},
     pages = {751--768},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {3},
     year = {1993},
     doi = {10.5802/aif.1354},
     mrnumber = {95f:35037},
     zbl = {0784.35023},
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}
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Palamodov, Victor P. Harmonic synthesis of solutions of elliptic equation with periodic coefficients. Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 751-768. doi : 10.5802/aif.1354. https://www.numdam.org/articles/10.5802/aif.1354/

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