Radelet, Dan
(2009)
Hardy-type sequence spaces and Cesaro frames.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Cesaro averaging is used in conjunction with Hardy space andHilbert space theory to realize certain types of convergence.In Chapter 1, we study certain Hardy-type sequence spaces, which are analogues ofell-infinity and c_0, respectively. We show that the Mazurproduct is not onto, which provides a new solution of Mazur's Problem 8 in the Scottish Book. We present corollaries for spaces defined via weighted ell-p seminorms and for c_0.In Chapter 2, we study the application of Cesaro operators onBessel sequences to realize a weak version of frame reconstructionin Hilbert space. Conditions for reconstruction via Markuschevichbases that are certain linear combinations of orthonormal basisvectors are given.
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Details
Item Type: |
University of Pittsburgh ETD
|
Status: |
Unpublished |
Creators/Authors: |
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ETD Committee: |
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Date: |
30 September 2009 |
Date Type: |
Completion |
Defense Date: |
30 July 2009 |
Approval Date: |
30 September 2009 |
Submission Date: |
10 August 2009 |
Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
Institution: |
University of Pittsburgh |
Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
Degree: |
PhD - Doctor of Philosophy |
Thesis Type: |
Doctoral Dissertation |
Refereed: |
Yes |
Uncontrolled Keywords: |
Cesaro frame; Banach space; Hardy space; averaging; frame |
Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-08102009-124755/, etd-08102009-124755 |
Date Deposited: |
10 Nov 2011 19:58 |
Last Modified: |
15 Nov 2016 13:48 |
URI: |
http://d-scholarship.pitt.edu/id/eprint/9041 |
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