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Müntz Space Embeddings of Schatten-Von Neumann Class

Thesis Info

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Author

Noor, Sahibzada Waleed

Supervisor

Dan Timotin

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2007

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2050/1/1710S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726737000

Similar


This thesis contains results about the embeddings of M ̈ untz spaces in the Hilbert space scenario and its applications to composition operators on M ̈ untz spaces. In the main, we shall be concerned with the embedding M Λ 2 ⊂ L 2 (μ), where the Hilbert- M ̈ untz space M Λ 2 is the closed linear span of the monomials x λ n in L 2 ([0, 1]) and μ is a finite Borel measure on [0, 1]. After gathering together the mathematical preliminaries required for this work in Chapter 1, we shall use the notion of a sublinear measure introduced by I. Chal- endar, E. Fricain and D. Timotin [8] to investigate the properties of boundedness, compactness and belonging to Schatten-von Neumann ideals of these Hilbert space embeddings. This will be the content of Chapters 2 and 3. In Chapter 4, we give ex- amples of sublinear measures for bounded and compact embeddings with interesting properties. Finally, in Chapter 5 the general embedding theory is applied to initiate the study of composition operators on M Λ 2 .
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