O'Reilly logo

A Primer on the Dirichlet Space by Thomas Ransford, Javad Mashreghi, Karim Kellay, Omar El-Fallah

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

8

Invariant subspaces

‘Invariant subspaces’ here refers to the closed subspaces invariant under the shift operator image The invariant subspaces of H2 were completely classified by Beurling, who showed that they are of the form θH2 for some inner function θ (together with the zero subspace). It is no exaggeration to say that Beurling’s theorem is one of the cornerstones of the whole theory of Hardy spaces. Our aim in this chapter is to obtain an analogous result in the Dirichlet space image.

One of the principal differences between H2 and is that, whereas ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required