Carl Sundberg

Beurling's Theorem for the Bergman space

A celebrated theorem in operator theory is A. Beurlings description of the invariant subspaces in

On the index of invariant subspaces in spaces of analytic functions of several complex variables

H^2

Generalized finite differences and Bayesian conditioning of Choquet capacities

in terms of inner functions [Acta Math. {\bf81} (1949), 239--255; MR0027954 (10,381e)]. To do the same thing for the Bergman space

THE MAJORIZATION FUNCTION AND THE INDEX OF INVARIANT SUBSPACES IN THE BERGMAN SPACES

L^2_a

Measures induced by analytic functions and a problem of Walter Rudin

has been deemed virtually impossible by many analysts, in view of the fact that the lattice of invariant subspaces is so large, and that the invariant subspaces may have weird properties as viewed from the

Harmonic measure and radial projection

H^2

Analytic contractions, nontangential limits, and the index of invariant subspaces

perspective. The size of the lattice can be appreciated from the known fact that essentially every operator on separable Hilbert space can be realized as the compression of the Bergman shift on

HARMONIC MEASURE OF CURVES IN THE DISK

M\ominus N

On the spectral problem for anyons

, where

A constructive proof of the Chang-Marshall theorem

M