| While bounded multiplication has been extensively researched, unbounded multiplication has received little attention until more recently. We develop a framework for densely defined multiplication over reproducing kernel Hilbert spaces, and we find an application toward extending reproducing kernels. We also extend a result of Allen Shields, who showed that the multipliers for the Sobolev space are precisely the elements of that space. We show that this holds even if multipliers are merely densely defined.;In connection with multiplication operators, we explore densely defined Toeplitz operators. Here we find simpler proofs of theorems from Sarason and Suarez. We also produce a partial answer to a problem posed by Donald Sarason by constructing an algorithm for recovering the symbol for a class of densely defined Toeplitz operators. |
