Unitary Perturbations of Compressed n-Dimensional Shifts

作者：Martin R T W^*

来源：Complex Analysis and Operator Theory, 2013, 7(4): 765-799.

DOI：10.1007/s11785-012-0236-8

• Hardy space
• Model subspaces
• Aleksandrov disintegration theorem
• Clark%26apos
• s unitary perturbations
• Aleksandrov-Clark measures
• Matrix-analytic functions
• Symmetric/isometric linear transformations

Given any contractive matrix-valued analytic function on the unit disc , we construct a -parameter family of unitary operators which correspond to in a natural way. These operators are unitarily equivalent to higher dimensional analogues of Clark%26apos;s unitary perturbations, a family of unitary operators associated to any self-map of the unit disc. Clark%26apos;s unitary perturbations were introduced in a seminal paper of Clark which has inspired the study of what are now called Aleksandrov-Clark measures. Our higher dimensional analogues of Clark%26apos;s unitary perturbations are applied to obtain matrix-generalizations of several classical results on the Aleksandrov-Clark measures associated to any holomorphic self-map of the unit disc. In particular we establish a matrix-valued Aleksandrov disintegration theorem for the Aleksandrov-Clark measures associated with matrix-valued contractive analytic functions , and, by following results of Clark and Fricain in the scalar case, we provide a necessary and sufficient condition for the de Branges-Rovnyak space associated with to contain a total orthogonal set of point evaluation vectors.

• 出版日期2013-8