Date of Award

Summer 2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics & Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Raymond Cheng

Committee Member

Gordon Melrose

Committee Member

Sandipan Dutta

Committee Member

Tim J. Anderson

Abstract

The space ℓp,α of complex sequences a = (a0,a1,a2, . . .) for which

∞

∥a∥p,α = ( Σ|ak|p(k+1)α)1/p < ∞

k=0

is studied. Each such sequence can be identified with the analytic function with power series

∞

f (z) = ∑ akzk.

k=0

In this setting, the point evaluation and the difference quotient mappings are shown to be bounded; the cases are identified in which ℓp,α is boundedly contained in ℓr,β . Conditions on the parameters are derived for the analytic functions of ℓp,α to have radial limits almost everywhere on the boundary of the domain, and for ℓp,α to be an algebra. Smoothness properties of the boundary function are investigated. Basic properties of multipliers on ℓp,α are established, and conditions on the multiplier norm and coefficient growth are derived. Multipliers having a certain extremal property are described. A discrete version of the Schur Test is obtained, and used to produce a family of examples of multipliers.

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In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

DOI

10.25777/2ppc-mw58

ISBN

9798384454595

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