Dichotomy and H^infinity functional calculi
densely defined closed operator on a Banach space is studied. We give conditions under which an operator with an $H^infty$ functional calculus has dichotomy. For the operators with imaginary axis contained in the resolvent set and with polynomial growth of the resolvent along the axis we prove the e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
1995-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1995/13/abstr.html |
| _version_ | 1818154823371980800 |
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| author | R. DeLaubenfels Y. Latushkin |
| author_facet | R. DeLaubenfels Y. Latushkin |
| author_sort | R. DeLaubenfels |
| collection | DOAJ |
| description | densely defined closed operator on a Banach space is studied. We give conditions under which an operator with an $H^infty$ functional calculus has dichotomy. For the operators with imaginary axis contained in the resolvent set and with polynomial growth of the resolvent along the axis we prove the existence of dichotomy on subspaces and superspaces. Applications to the dichotomy of operators on $L_p$-spaces are given. The principle of linearized instability for nonlinear equations is proved. |
| first_indexed | 2024-12-11T14:32:38Z |
| format | Article |
| id | doaj.art-51975003fcd04e2e80ef8e000e55bc9d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T14:32:38Z |
| publishDate | 1995-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-51975003fcd04e2e80ef8e000e55bc9d2022-12-22T01:02:20ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911995-09-01199513117Dichotomy and H^infinity functional calculiR. DeLaubenfelsY. Latushkindensely defined closed operator on a Banach space is studied. We give conditions under which an operator with an $H^infty$ functional calculus has dichotomy. For the operators with imaginary axis contained in the resolvent set and with polynomial growth of the resolvent along the axis we prove the existence of dichotomy on subspaces and superspaces. Applications to the dichotomy of operators on $L_p$-spaces are given. The principle of linearized instability for nonlinear equations is proved.http://ejde.math.txstate.edu/Volumes/1995/13/abstr.htmlAbstract Cauchy problemoperator semigroupsexponential dichotomyfunctional calculi. |
| spellingShingle | R. DeLaubenfels Y. Latushkin Dichotomy and H^infinity functional calculi Electronic Journal of Differential Equations Abstract Cauchy problem operator semigroups exponential dichotomy functional calculi. |
| title | Dichotomy and H^infinity functional calculi |
| title_full | Dichotomy and H^infinity functional calculi |
| title_fullStr | Dichotomy and H^infinity functional calculi |
| title_full_unstemmed | Dichotomy and H^infinity functional calculi |
| title_short | Dichotomy and H^infinity functional calculi |
| title_sort | dichotomy and h infinity functional calculi |
| topic | Abstract Cauchy problem operator semigroups exponential dichotomy functional calculi. |
| url | http://ejde.math.txstate.edu/Volumes/1995/13/abstr.html |
| work_keys_str_mv | AT rdelaubenfels dichotomyandhinfinityfunctionalcalculi AT ylatushkin dichotomyandhinfinityfunctionalcalculi |