Digital Commons Network^™

Connected Inverse Limits With A Set-Valued Function, Van C. Nall

Department of Math & Statistics Faculty Publications

In this paper we provide techniques to build set-valued functions whose resulting inverse limits will be connected.

Inverse Limits With Set Valued Functions, Van C. Nall

Department of Math & Statistics Faculty Publications

We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [O, 1) to 2^(O,l). Several continua including (0, 1) x (0, 1) and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.

The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H² and H^∞ norms of functions in model spaces.

Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen

Department of Math & Statistics Faculty Publications

In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H²ƟBH², where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions - in terms of the matrix representation - of when a linear transformation on H²ƟBH² is the compression of a Toeplitz operator. This result complements a related result of Sarason [6].

Indestructible Blaschke Products, William T. Ross

Department of Math & Statistics Faculty Publications

No abstract provided.

Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg

Department of Math & Statistics Faculty Publications

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

Common Cyclic Vectors For Normal Operators, William T. Ross, Warren R. Wogen

Department of Math & Statistics Faculty Publications

If μis a finite compactly supported measure on C, then the set S_μ of multiplication operators Mᵩ : L² (μ) --> L² (μ), Mᵩ f = ᵩ f, where ᵩ ϵ L ∞ (μ) is injective on a set of full μ measure, is the complete set of cyclic multiplication operators on L² (μ) In this paper, we explore the question as to whether or not S_μ has a common cyclic vector

The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson

Department of Math & Statistics Faculty Publications

This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --> z^-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.

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 …

Invariant Subspaces Of The Harmonic Dirichlet Space With Large Co-Dimension, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f → ζf) of the harmonic Dirichlet space D. Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces F ⊂ D with dim(F/ζF) = n, n ∈ N ∪ {∞}. We will also generalize this to the Dirichlet classes Dα, 0 <α< ∞, as well as the Besov classes B^α _p , 1

Analytic Besov Spaces And Invariant Subspaces Of Bergman Spaces, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we examine the invariant subspaces (under the operator f -->z f) M of the Bergman space ^p_a (G\T) (where 1 < p < 2, G is a bounded region in C containing D, T is the unit circle, and D is the unit disk) which contain the characteristic functions x_D and x_G, i.e. the constant functions on the components of G\T. We will show that such M are in one-to-one correspondence with the invariant subspaces of the analytic Besov space AB_q (q is the conjugate index to p) and …

Invariant Subspaces Of Bergman Spaces On Slit Domains, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we characterize the z-invariant subspaces that lie between the Bergman spaces A^p(G) and A^p(G\K), where 1 < p < ∞, G is a bounded region in C, and K is a closed subset of a simple, compact, C¹ arc.

The Commutant Of A Certain Compression, William T. Ross

Department of Math & Statistics Faculty Publications

Let G be any bounded region in the complex plane and K Ϲ G be a simple compact arc of class C¹. Let A²(G\K) (resp. A²(G)) be the Bergman space on G\K (resp. G). Let S be the operator multiplication by z on A²(G\K) and C = P_N S│_N be the compression of S to the semi-invariant subspace N = A²(G\K) Ɵ A²(G). We show that the commutant of C* is the set of all operators …

Analytic Continuation In Bergman Spaces And The Compression Of Certain Toeplitz Operators, William T. Ross

Department of Math & Statistics Faculty Publications

Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A² (G\K) and A²(G) be the Bergman spaces on G\K, respectively G and define N = A²(G\K) Ɵ A² (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of aG that do not intersect K. This result will be used to discuss the Fredholm theory of the operator C_f = P_NT_f│N, where f ϵ C(G) …

On Uniform And Relative Distribution In The Brauer Group, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

In this progress/technical report our objective is twofold. First, to formalize and expand upon remarks appearing in [7] concerning the relativization of the fundamental identity in the setting of the Brauer group of a ring, and second to exhibit a construction which shows how to interpret uniform distribution as a homological phenomenon.

Partially Confluent Maps And N-Ods, Van C. Nall

Department of Math & Statistics Faculty Publications

Let f : X-->Y be a map between topological spaces. A Wf-set in Y is a continuum in Y which is the image under f of a continuum in X. The map f is partially confluent if each continuum in Y is the union of a finite number of Wf-sets, and n-partially confluent if each continuum in Y is the union of n Wf-sets. In this paper, it is shown that every partially confluent map onto an n-cell is weakly confluent. Also, the relationship between partially confluent maps and continua which …