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Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates
We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncomm...
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| Published in: | Annales Henri Poincaré 2016-05, Vol.17 (5), p.1181-1208 |
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| Main Authors: | , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c316t-9b387863dc8c24b8d92eeb01d9c568992bffd3f2e7e286e839fbac5a06e48b723 |
| container_end_page | 1208 |
| container_issue | 5 |
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| container_title | Annales Henri Poincaré |
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| creator | Krueger, August J. Soffer, Avy |
| description | We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We prove pointwise in time decay estimates with the decay rate
t
-
1
log
-
2
t
, which is optimal with the chosen weights and appears to be so generally. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate. |
| doi_str_mv | 10.1007/s00023-015-0431-z |
| format | article |
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t
-
1
log
-
2
t
, which is optimal with the chosen weights and appears to be so generally. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate.</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-015-0431-z</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Classical and Quantum Gravitation ; Decay rate ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Field theory ; Finite differences ; Functions (mathematics) ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Polynomials ; Quantum Field Theory ; Quantum Physics ; Relativity Theory ; Schrodinger equation ; Solitary waves ; Spectral theory ; Theoretical</subject><ispartof>Annales Henri Poincaré, 2016-05, Vol.17 (5), p.1181-1208</ispartof><rights>Springer Basel 2015</rights><rights>2015© Springer Basel 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-9b387863dc8c24b8d92eeb01d9c568992bffd3f2e7e286e839fbac5a06e48b723</citedby><cites>FETCH-LOGICAL-c316t-9b387863dc8c24b8d92eeb01d9c568992bffd3f2e7e286e839fbac5a06e48b723</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Krueger, August J.</creatorcontrib><creatorcontrib>Soffer, Avy</creatorcontrib><title>Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We prove pointwise in time decay estimates with the decay rate
t
-
1
log
-
2
t
, which is optimal with the chosen weights and appears to be so generally. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate.</description><subject>Classical and Quantum Gravitation</subject><subject>Decay rate</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Field theory</subject><subject>Finite differences</subject><subject>Functions (mathematics)</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Polynomials</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Schrodinger equation</subject><subject>Solitary waves</subject><subject>Spectral theory</subject><subject>Theoretical</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEqXwAewssQ74kToOO9QHVKroomVtOc4EUjVxsF2k9utxFAQrVjOLc--MDkK3lNxTQrIHTwhhPCF0kpCU0-R0hkY0ZWlChKDnvzvPLtGV9ztCKJM8H6H17NjqpjYe2wq_2tbYpjkEHeovwBu7r4NtPV4-4k0HJji9x9sPsO6IdVviWe07cL5H5z7UjQ7gr9FFpfcebn7mGL0t5tvpS7JaPy-nT6vEcCpCkhdcZlLw0kjD0kKWOQMoCC1zMxEyz1lRVSWvGGTApID4alVoM9FEQCqLjPExuht6O2c_D-CD2tmDa-NJxXjKmYjtPUUHyjjrvYNKdS7-6Y6KEtV7U4M3Fb2p3ps6xQwbMj6y7Tu4v-b_Q9_2lXEH</recordid><startdate>20160501</startdate><enddate>20160501</enddate><creator>Krueger, August J.</creator><creator>Soffer, Avy</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160501</creationdate><title>Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates</title><author>Krueger, August J. ; Soffer, Avy</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-9b387863dc8c24b8d92eeb01d9c568992bffd3f2e7e286e839fbac5a06e48b723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Decay rate</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Field theory</topic><topic>Finite differences</topic><topic>Functions (mathematics)</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Polynomials</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Schrodinger equation</topic><topic>Solitary waves</topic><topic>Spectral theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Krueger, August J.</creatorcontrib><creatorcontrib>Soffer, Avy</creatorcontrib><collection>CrossRef</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krueger, August J.</au><au>Soffer, Avy</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2016-05-01</date><risdate>2016</risdate><volume>17</volume><issue>5</issue><spage>1181</spage><epage>1208</epage><pages>1181-1208</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We prove pointwise in time decay estimates with the decay rate
t
-
1
log
-
2
t
, which is optimal with the chosen weights and appears to be so generally. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00023-015-0431-z</doi><tpages>28</tpages></addata></record> |
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| ispartof | Annales Henri Poincaré, 2016-05, Vol.17 (5), p.1181-1208 |
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| language | eng |
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| subjects | Classical and Quantum Gravitation Decay rate Dynamical Systems and Ergodic Theory Elementary Particles Field theory Finite differences Functions (mathematics) Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Operators (mathematics) Physics Physics and Astronomy Polynomials Quantum Field Theory Quantum Physics Relativity Theory Schrodinger equation Solitary waves Spectral theory Theoretical |
| title | Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates |
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