Some Problems in the Spectral Theory of Separated Dirac Operators: A representation of the spectral function of a Dirac operator and a bound for points of spectral concentration

Eggenberger, Joshua T.

ISBN 10: 384733767X / ISBN 13: 9783847337676

Published by LAP LAMBERT Academic Publishing, 2012

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Bibliographic Details

• Title: Some Problems in the Spectral Theory of Separated Dirac Operators: A representation of the spectral function of a Dirac operator and a bound for points of spectral concentration
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2012
• Language: English
• ISBN 10: 384733767X
• ISBN 13: 9783847337676
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

This work describes a representation of the spectral function for the Dirac operator, and includes an application of this representation to the problem of bounding the points of spectral concentration of the operator. Conditions on the potential function under which an absolutely continuous spectrum exists are given. A connection is made between the Dirac system and a Riccati equation, and the spectral derivative is expressed using a series solution of the Riccati equation. Conditions under which this series converges are given. The terms of the series are then differentiated to obtain a representation of the second derivative of the spectral function. The question of relative asymptotic sizes of the terms of this representation are addressed. The construction and application of the representation are similar to those used to investigate the spectrum of the Sturm-Liouville operator.

About the Author

Dr. Joshua Eggenberger received his PhD in mathematical science from Northern Illinois University in 2010. He has taught undergraduate mathematics courses at NIU, Kishwaukee College, and Anoka-Ramsey Community College, and is currently an assistant professor at Ashford University in Clinton, Iowa.