@article{Mikhailets_Murach_2013, title={Extended Sobolev Scale and Elliptic Operators}, volume={65}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2426}, abstractNote={We obtain a constructive description of all Hilbert function spaces that are interpolation spaces with respect to a couple of Sobolev spaces $[H^{(s_0)}(\mathbb{R}^n), H^{(s_1)}(\mathbb{R}^n)]$ of some integer orders $s_0$ and $s_1$ and that form an extended Sobolev scale. We find equivalent definitions of these spaces with the use of uniformly elliptic pseudodifferential operators positive definite in $L_2(\mathbb{R}^n)$. Possible applications of the introduced scale of spaces are indicated.}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Mikhailets, V. A. and Murach, A. A.}, year={2013}, month={Mar.}, pages={392-404} }