Characterization of Beals spaces

In the last decade a class of spaces introduced by Richard Beals in 1965 was frequently used as “natural” domains of symmetric properly elliptic differential operators in extension theory methods in Hilbert spaces. In the present note we use some fundamental results from Lions and Magenes to show that the so-called Beals spaces coincide with usual Sobolev spaces endowed with the graph norm of a properly elliptic differential operator. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)