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Elliptic systems of pseudodifferential equations in the refined scale on a closed manifold

Mikhailets V. A., Murach A. A.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 3-4

213-224

We study a system of pseudodifferential equations which is elliptic in the Petrovskiî sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.