Parameter-elliptic operators on the extended Sobolev scale

Authors

  • T. Zinchenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine
  • A. A. Murach Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

DOI:

Keywords:

Parameter–elliptic operator, extended Sobolev scale, H¨ormander space, ROvarying function, interpolation with function parameter, isomorphism property, a priory estimate ofsolutions

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.

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Published

2013-03-25

Issue

Vol. 19 No. 1 (2013)

Section

Articles

How to Cite

Zinchenko, T., and A. A. Murach. “Parameter-Elliptic Operators on the Extended Sobolev Scale”. Methods of Functional Analysis and Topology, vol. 19, no. 1, Mar. 2013, pp. 29-39, https://zen.imath.kiev.ua/index.php/mfat/article/view/533.