Abstract/Details

Hermite/Laguerre-Gaussian modes & lower bounds for quasimodes of semiclassical operators


2009 2009

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Abstract (summary)

In the first part of the dissertation, we are concerned with local lower bounds for (i) quasimodes of semiclassical Schrödinger operators on domains with boundary and for (ii) Bargmann transforms of certain functions. On domains with boundary, the main tool is a boundary Carleman estimate, essentially due to Lebeau and Robbiano. It is more elementary to prove lower bounds for Bargmann transforms, since Bargmann transforms map to weighted spaces of holomorphic functions.

In the second part of the dissertation, we study the manipulation of Hermite-Gaussian modes and Laguerre-Gaussian modes for use in laser physics, building on the work of Calvo and Picón. Specifically, we classify the self-adjoint extensions of Calvo and Picón's operators, and we study the associated unitary propagators using methods from semiclassical analysis.

Indexing (details)


Subject
Mathematics;
Optics
Classification
0405: Mathematics
0752: Optics
Identifier / keyword
Pure sciences; Bargmann transforms; Carleman estimates; Hermite-Gaussian modes; Quasimodes; Semiclassical operators
Title
Hermite/Laguerre-Gaussian modes & lower bounds for quasimodes of semiclassical operators
Author
VanValkenburgh, Michael James
Number of pages
156
Publication year
2009
Degree date
2009
School code
0031
Source
DAI-B 70/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109470505
Advisor
Hitrik, Michael
University/institution
University of California, Los Angeles
University location
United States -- California
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3384020
ProQuest document ID
304852256
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304852256
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