Geodesic
Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold
Vladimir A. Mikhailets 1   ; Aleksandr A. Murach 2
1 Institute of Mathematics NAS of Ukraine Tereshchenkivska St. 3 Kyiv 01601, Ukraine
2 Institute of Mathematics NAS of Ukraine Tereshchenkivska St. 3 Kyiv 01601, Ukraine and Chernigiv State Technological University Shevchenka St. 95 Chernigiv 14027, Ukraine
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 3, pp. 213-224 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba56-3-4
Keywords: study system pseudodifferential equations which elliptic petrovskii sense closed smooth manifold prove operator generated system fredholm operator refined two sided scale hilbert function spaces elements scale special isotropic spaces rmander volevich paneah

Vladimir A. Mikhailets  1   ; Aleksandr A. Murach  2

1 Institute of Mathematics NAS of Ukraine Tereshchenkivska St. 3 Kyiv 01601, Ukraine
2 Institute of Mathematics NAS of Ukraine Tereshchenkivska St. 3 Kyiv 01601, Ukraine and Chernigiv State Technological University Shevchenka St. 95 Chernigiv 14027, Ukraine 
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     author = {Vladimir A. Mikhailets and Aleksandr A. Murach},
     title = {Elliptic {Systems} {of
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     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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Vladimir A. Mikhailets; Aleksandr A. Murach. Elliptic Systems of
Pseudodifferential Equations in the Refined Scale on a Closed Manifold. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 3, pp. 213-224. doi: 10.4064/ba56-3-4

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