Generalized powers and measures

Abstract

Using the winding of measures on torus in "rational directions" special classes of unitary operators and pairs of isometries are defined. This provides nontrivial examples of generalized powers. Operators related to winding Szegö-singular measures are shown to have specific properties of their invariant subspaces.

Keywords

• representing measures
• szegö-singular measure
• compatible pair of isometries
• spectral measure