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 - Softcover
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.
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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.
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Some Problems in the Spectral Theory of Separated Dirac Operators
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LAP LAMBERT Academic Publishing Jan 2012, 2012
ISBN 10: 384733767X
ISBN 13: 9783847337676
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 72 pp. Englisch. Seller Inventory # 9783847337676
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Some Problems in the Spectral Theory of Separated Dirac Operators
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ISBN 10: 384733767X
ISBN 13: 9783847337676
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Eggenberger Joshua T.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 Co. Seller Inventory # 5511012
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Some Problems in the Spectral Theory of Separated Dirac Operators
Published by
LAP LAMBERT Academic Publishing Jan 2012, 2012
ISBN 10: 384733767X
ISBN 13: 9783847337676
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 72 pp. Englisch. Seller Inventory # 9783847337676
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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
Published by
LAP LAMBERT Academic Publishing, 2012
ISBN 10: 384733767X
ISBN 13: 9783847337676
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Seller Inventory # 9783847337676
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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
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ISBN 10: 384733767X
ISBN 13: 9783847337676
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Taschenbuch. Condition: Neu. 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 | Joshua T. Eggenberger | Taschenbuch | 72 S. | Englisch | 2012 | LAP LAMBERT Academic Publishing | EAN 9783847337676 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu. Seller Inventory # 106649035
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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
Published by
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ISBN 10: 384733767X
ISBN 13: 9783847337676
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