TY - JOUR AU - V. A. Mikhailets AU - A. A. Murach PY - 2013/03/25 Y2 - 2024/03/29 TI - Extended Sobolev Scale and Elliptic Operators JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 65 IS - 3 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2426 AB - 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. ER -