Abstract: | Let ![OHgr](/content/jg4l5m134w270473/xxlarge937.gif) R3 be a bounded domain, , a family of extending subdomains, and = (x) a positive function in be a space of -solenoidal vector fields, , a family of subspaces, G orthogonal projectors in onto . A unitary transformation that diagonalizes the family of projectors {G } is constructed: it takes to the operator of multiplication by the independent variable. The isometry of this transformation is proved with the help of the operator Riccati equation for the Neumann to Dirichlet mapping. Bibliography: 8 titles. |