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Synopsis
In these notes, a theory for sesquilinear forms on product spaces is developed, with the aim of unifying the treatment of diffusion systems and equation on networks. In the first part, a theoretical framework for sesquilinear forms defined on the direct sum of Hilbert spaces is developed. Conditions for the boundedness, ellipticity and coercivity of the sesquilinear form are proved. A criterion of E.-M. Ouhabaz is used in order to prove qualitative properties of the abstract Cauchy problem having as generator the operator associated with the sesquilinear form. In the second part we analyze quantum graphs as a special case of forms on subspaces of the direct sum of Hilbert spaces. First, we set up a framework for handling quantum graphs in the case of infinite networks. Then, the operator associated with such systems is identified and investigated. Finally, we turn our attention to symmetry properties of the associated parabolic problem and we investigate the connection with the physical concept of a gauge symmetry.
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About the Author
Studied Mechanical Engineering and Mathematics at the Universities of Bari (Italy) and Tübingen (Germany) from 1998 to 2005. He obtained a diploma in Mathematics in September 2005. He completed his PhD studies at the University of Ulm (2005-2008). He obtained his PhD degree in June 2008. Since May 2008 he is a PostDoc at the BCCN Freiburg.
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- PublisherSuedwestdeutscher Verlag fuer Hochschulschriften
- Publication date2010
- ISBN 10 3838113160
- ISBN 13 9783838113166
- BindingPaperback
- LanguageEnglish
- Number of pages116
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Diffusion systems and heat equations on networks
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Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG Okt 2015, 2015
ISBN 10: 3838113160
ISBN 13: 9783838113166
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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In these notes, a theory for sesquilinear forms on product spaces is developed, with the aim of unifying the treatment of diffusion systems and equation on networks. In the first part, a theoretical framework for sesquilinear forms defined on the direct sum of Hilbert spaces is developed. Conditions for the boundedness, ellipticity and coercivity of the sesquilinear form are proved. A criterion of E.-M. Ouhabaz is used in order to prove qualitative properties of the abstract Cauchy problem having as generator the operator associated with the sesquilinear form. In the second part we analyze quantum graphs as a special case of forms on subspaces of the direct sum of Hilbert spaces. First, we set up a framework for handling quantum graphs in the case of infinite networks. Then, the operator associated with such systems is identified and investigated. Finally, we turn our attention to symmetry properties of the associated parabolic problem and we investigate the connection with the physical concept of a gauge symmetry. 116 pp. Englisch. Seller Inventory # 9783838113166
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Diffusion systems and heat equations on networks : Symmetries and irreducibility
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Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG, 2010
ISBN 10: 3838113160
ISBN 13: 9783838113166
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Seller: AHA-BUCH GmbH, Einbeck, Germany
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - In these notes, a theory for sesquilinear forms on product spaces is developed, with the aim of unifying the treatment of diffusion systems and equation on networks. In the first part, a theoretical framework for sesquilinear forms defined on the direct sum of Hilbert spaces is developed. Conditions for the boundedness, ellipticity and coercivity of the sesquilinear form are proved. A criterion of E.-M. Ouhabaz is used in order to prove qualitative properties of the abstract Cauchy problem having as generator the operator associated with the sesquilinear form. In the second part we analyze quantum graphs as a special case of forms on subspaces of the direct sum of Hilbert spaces. First, we set up a framework for handling quantum graphs in the case of infinite networks. Then, the operator associated with such systems is identified and investigated. Finally, we turn our attention to symmetry properties of the associated parabolic problem and we investigate the connection with the physical concept of a gauge symmetry. Seller Inventory # 9783838113166
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Diffusion systems and heat equations on networks
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Südwestdeutscher Verlag für Hochschulschriften, 2015
ISBN 10: 3838113160
ISBN 13: 9783838113166
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Seller: moluna, Greven, Germany
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In these notes, a theory for sesquilinear forms on product spaces is developed, with the aim of unifying the treatment of diffusion systems and equation on networks. In the first part, a theoretical framework for sesquilinear forms defined on the direct sum. Seller Inventory # 5405692
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