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# Douglis-Nirenberg elliptic systems in the refined scale of spaces on a closed manifold

### Abstract

Douglis-Nirenberg elliptic systems of linear pseudodifferential equations are studied on a smooth closed manifold. We prove that the operator generated by the system is a Fredholm one on the refined two-sided scale of the functional Hilbert spaces. Elements of this scale are the special isotropic spaces of H\"{o}rmander-Volevich-Paneah. The refined smoothness of a solution of the system is studied. The elliptic systems with a parameter are investigated as well.

### Article Information

 Title Douglis-Nirenberg elliptic systems in the refined scale of spaces on a closed manifold Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 2, 142-158 MathSciNet MR2432763 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Aleksandr A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine; Chernigiv State Technological University, 95 Shevchenka, Chernigiv, 14027, Ukraine

### Citation Example

Aleksandr A. Murach, Douglis-Nirenberg elliptic systems in the refined scale of spaces on a closed manifold, Methods Funct. Anal. Topology 14 (2008), no. 2, 142-158.

### BibTex

@article {MFAT456,
AUTHOR = {Murach, Aleksandr A.},
TITLE = {Douglis-Nirenberg elliptic systems in the refined scale of spaces on a closed manifold},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {2},
PAGES = {142-158},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=456},
}