A spectral theory for inner functions

Malcolm J. Sherman
1969 Transactions of the American Mathematical Society  
Let ty be an inner function in the sense of Lax; i.e., ty(ew) is almost everywhere a unitary operator on a separable Hubert space ¿€, and ty belongs weakly to the Hardy class Ü2. Inner functions arise from subspaces of H%, invariant under the right shift operator ("invariant subspaces") and from bounded operators on JÍ? in ways to be specified. We are interested in finding canonical forms for and invariants of inner functions, and where an inner function comes from an operator on Jf, in
more » ... r on Jf, in relating the invariants of the inner function to those of the operator. For basic definitions and notations consult [5, particularly Chapter VI], or [15] .
doi:10.1090/s0002-9947-1969-0236743-x fatcat:tiscfqe5o5cbdog7ei5es3tawe