Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold

Volume 56 / 2008

Vladimir A. Mikhailets, Aleksandr A. Murach Bulletin Polish Acad. Sci. Math. 56 (2008), 213-224 MSC: Primary 35J45; Secondary 46E35. DOI: 10.4064/ba56-3-4

Abstract

We study a system of pseudodifferential equations which is elliptic in the Petrovskii 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.

Authors

  • Vladimir A. MikhailetsInstitute of Mathematics NAS of Ukraine
    Tereshchenkivska St. 3
    Kyiv 01601, Ukraine
    e-mail
  • Aleksandr A. MurachInstitute of Mathematics NAS of Ukraine
    Tereshchenkivska St. 3
    Kyiv 01601, Ukraine
    and
    Chernigiv State Technological University
    Shevchenka St. 95
    Chernigiv 14027, Ukraine
    e-mail

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