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A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia
A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia
Pomona Faculty Publications and Research
We study real Smirnov functions and investigate a certain *-closed subalgebra of the Smirnov class N^+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space H^p ∩ H^p [overscore over the second H^p]. This leads to a natural analog of the Riesz projection on a certain quotient space of L^p for p ϵ (0, 1). We also study a Herglotz-like integral transform for singular measures on the unit circle ∂D.
Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia
Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia
Pomona Faculty Publications and Research
We describe and parameterize the solutions of the scalar valued Darlington synthesis problem. In the case of rational data we derive a simple procedure for producing all possible solutions.
Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro
Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro
Department of Math & Statistics Faculty Publications
For functions belonging to invariant subspaces of the backward shift operator Bf = (f − f(0))/z on spaces of analytic functions on the unit disk D, we explore, in a systematic way, the continuation properties of these functions.