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The Backward Shift On HP, William T. Ross
The Backward Shift On HP, William T. Ross
Department of Math & Statistics Faculty Publications
In this semi-expository paper, we examine the backward shift operator
Bf := (f-f(0)/z
on the classical Hardy space Hp. Through there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds Ɛ ⊂ Hp for which BƐ ⊂ Ɛ. When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation developed earlier by Shapiro [26]. When p = 1, the description is the same [1] except that in the proof, one must be mindful of some technical considerations involving the functions of bounded mean oscillation.
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.
Pseudocontinuations And The Backward Shift, William T. Ross, Alexandru Aleman, Stefan Richter
Pseudocontinuations And The Backward Shift, William T. Ross, Alexandru Aleman, Stefan Richter
Department of Math & Statistics Faculty Publications
In this paper, we will examine the backward shift operator Lf = (f −f(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM Ϲ M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L│M. In order to do this, we will use the concept of “pseudocontinuation" of functions across the unit circle T.
We will first discuss the backward shift on a general Banach space of analytic functions and then for the weighted …
Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross
Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross
Department of Math & Statistics Technical Report Series
In this paper, we will examine the backward shift operator Lƒ = (ƒ – ƒ(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂ M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of "pseudocontinuation" of functions across the unit circle ∏.