Convexity, boundedness, and almost periodicity for differential equations in Hillbert space
There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator...
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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000016 |
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| _version_ | 1832545504995573760 |
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| author | Jerome A. Goldstein |
| author_facet | Jerome A. Goldstein |
| author_sort | Jerome A. Goldstein |
| collection | DOAJ |
| description | There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost periodic. |
| format | Article |
| id | doaj-art-50c7778c449c42aa862fd400df14ece3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-50c7778c449c42aa862fd400df14ece32025-02-03T07:25:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012111310.1155/S0161171279000016Convexity, boundedness, and almost periodicity for differential equations in Hillbert spaceJerome A. Goldstein0Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USAThere are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost periodic.http://dx.doi.org/10.1155/S0161171279000016differential equations in Hilbert spaceconvexity inequalityself-adjoint operatorsbounded solutionsalmost periodic solutions. |
| spellingShingle | Jerome A. Goldstein Convexity, boundedness, and almost periodicity for differential equations in Hillbert space International Journal of Mathematics and Mathematical Sciences differential equations in Hilbert space convexity inequality self-adjoint operators bounded solutions almost periodic solutions. |
| title | Convexity, boundedness, and almost periodicity for differential equations in Hillbert space |
| title_full | Convexity, boundedness, and almost periodicity for differential equations in Hillbert space |
| title_fullStr | Convexity, boundedness, and almost periodicity for differential equations in Hillbert space |
| title_full_unstemmed | Convexity, boundedness, and almost periodicity for differential equations in Hillbert space |
| title_short | Convexity, boundedness, and almost periodicity for differential equations in Hillbert space |
| title_sort | convexity boundedness and almost periodicity for differential equations in hillbert space |
| topic | differential equations in Hilbert space convexity inequality self-adjoint operators bounded solutions almost periodic solutions. |
| url | http://dx.doi.org/10.1155/S0161171279000016 |
| work_keys_str_mv | AT jeromeagoldstein convexityboundednessandalmostperiodicityfordifferentialequationsinhillbertspace |