Extended Sobolev Scale and Elliptic Operators - Mikhailets, V. A.; Murach, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
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)(R^n), H^(s_1)(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(R^n). Possible applications of the introduced scale of spaces are indicated.