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# Parameter-elliptic operators on the extended Sobolev scale

### Abstract

Parameter-elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to a Hilbert-Sobolev scale. We prove that these operators set isomorphisms between appropriate spaces of the scale provided the absolute value of the parameter is large enough. For solutions to the corresponding parameter-elliptic equations, we establish two-sided a priori estimates, in which the constants are independent of the parameter.

Key words: Parameter–elliptic operator, extended Sobolev scale, H¨ormander space, ROvarying function, interpolation with function parameter, isomorphism property, a priory estimate of solutions.

### Article Information

 Title Parameter-elliptic operators on the extended Sobolev scale Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 29-39 MathSciNet MR3088076 zbMATH 1289.58011 Milestones Received 03/12/2012 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

Aleksandr A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Tetiana Zinchenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Aleksandr A. Murach and Tetiana Zinchenko, Parameter-elliptic operators on the extended Sobolev scale, Methods Funct. Anal. Topology 19 (2013), no. 1, 29-39.

### BibTex

@article {MFAT676,
AUTHOR = {Murach, Aleksandr A. and Zinchenko, Tetiana},
TITLE = {Parameter-elliptic operators on the extended Sobolev scale},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {1},
PAGES = {29-39},
ISSN = {1029-3531},
MRNUMBER = {MR3088076},
ZBLNUMBER = {1289.58011},
URL = {http://mfat.imath.kiev.ua/article/?id=676},
}