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- Composition operator (2)
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- Banach spaces (1)
- Component structure (1)
- Composition operator; Adjoint; Hardy space (1)
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- Composition operator; Dirichlet space (1)
- Dual bases (1)
- Earle-Hamilton fixed-point theorem (1)
- Essential norm (1)
- Holomorphic functions (1)
- Jacobi triple product identity (1)
- Lumer-Phillips theorem (1)
- Multiresolution analyses (1)
- Norm (1)
- Quintuple product identity (1)
- Refinable vectors (1)
- Scaling vectors (1)
- Schroter's formula (1)
- Septuple product identity (1)
- Winquist's identity (1)
Articles 1 - 10 of 10
Full-Text Articles in Analysis
A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin
A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin
Mathematics Faculty Publications
We prove a generalization of Schroter's formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the well-known identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist's Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q)(infinity) and (q; q)(infinity)(k), k >= 3, as combinations of Jacobi triple products, are also proved.
Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock
Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock
Mathematics Faculty Publications
No abstract provided.
Sublimital Analysis, Thomas Q. Sibley
Sublimital Analysis, Thomas Q. Sibley
Mathematics Faculty Publications
The Bolzano-Weierstrass theorem asserts, under appropriate circumstances, the convergence of some subsequence of a sequence. While this famous theorem ignores the actual limit of the subsequence, it is natural to investigate such limits. This note characterizes the set of possible limits of subsequences of a given sequence.
Adjoints Of Composition Operators With Rational Symbol, Christopher Hammond, Jennifer Moorhouse, Marian Robbins
Adjoints Of Composition Operators With Rational Symbol, Christopher Hammond, Jennifer Moorhouse, Marian Robbins
Mathematics Faculty Publications
Building on techniques developed by C. C. Cowen and E. A. Gallardo-Gutiérrez [J. Funct. Anal. 238 (2006), no. 2, 447–462;MR2253727 (2007e:47033)], we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H 2 . We consider some specific examples, comparing our formula with several results that were previously known.
Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond
Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond
Mathematics Faculty Publications
We prove that any composition operator with maximal norm on one of the weighted Bergman spaces is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space H2, where every inner function induces a composition operator with maximal norm.
Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer
Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer
Mathematics Faculty Publications
We establish a condition that guarantees isolation in the space of composition operators acting between H p (B N ) and H q (B N ), for 0 < p ≤ ∞, 0 < q < ∞, and N ≥ 1. This result will allow us, in certain cases where 0 < q < p ≤ ∞, completely to characterize the component structure of this space of operators.
The Norm Of A Composition Operator With Linear Symbol Acting On The Dirichlet Space, Christopher Hammond
The Norm Of A Composition Operator With Linear Symbol Acting On The Dirichlet Space, Christopher Hammond
Mathematics Faculty Publications
We obtain a representation for the norm of a composition operator on the Dirichlet space induced by a map of the form φ(z)=az+b. We compare this result to an upper bound for ‖Cφ‖ that is valid whenever φ is univalent. Our work relies heavily on an adjoint formula recently discovered by Gallardo-Gutiérrez and Montes-Rodríguez.
Norms Of Linear-Fractional Composition Operators, Paul S. Bourdon, E. E. Fry, Christopher Hammond, C. H. Spofford
Norms Of Linear-Fractional Composition Operators, Paul S. Bourdon, E. E. Fry, Christopher Hammond, C. H. Spofford
Mathematics Faculty Publications
No abstract provided.
Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris
Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris
Mathematics Faculty Publications
We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.
A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler
A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler
Mathematics Faculty Publications
In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the …