On an abstract evolution equation with a spectral operator of scalar type
It is shown that the weak solutions of the evolution equation y′(t)=Ay(t), t∈[0,T) (0<T≤∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t)=e tAf, t∈[0,T), with the exponentials understood in the sense of the operati...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202112233 |
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| _version_ | 1850238046405918720 |
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| author | Marat V. Markin |
| author_facet | Marat V. Markin |
| author_sort | Marat V. Markin |
| collection | DOAJ |
| description | It is shown that the weak solutions of the evolution equation y′(t)=Ay(t), t∈[0,T) (0<T≤∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t)=e tAf, t∈[0,T), with the exponentials understood in the sense of the operational calculus for such operators and the set of the initial values, f's, being ∩ 0≤t<TD(e tA), that is, the largest possible such a set in X. |
| format | Article |
| id | doaj-art-084f8a2bdbed4d70a4d6586ec7b8fe3a |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-084f8a2bdbed4d70a4d6586ec7b8fe3a2025-08-20T02:01:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0132955556310.1155/S0161171202112233On an abstract evolution equation with a spectral operator of scalar typeMarat V. Markin0Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston 02215, MA, USAIt is shown that the weak solutions of the evolution equation y′(t)=Ay(t), t∈[0,T) (0<T≤∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t)=e tAf, t∈[0,T), with the exponentials understood in the sense of the operational calculus for such operators and the set of the initial values, f's, being ∩ 0≤t<TD(e tA), that is, the largest possible such a set in X.http://dx.doi.org/10.1155/S0161171202112233 |
| spellingShingle | Marat V. Markin On an abstract evolution equation with a spectral operator of scalar type International Journal of Mathematics and Mathematical Sciences |
| title | On an abstract evolution equation with a spectral operator of scalar type |
| title_full | On an abstract evolution equation with a spectral operator of scalar type |
| title_fullStr | On an abstract evolution equation with a spectral operator of scalar type |
| title_full_unstemmed | On an abstract evolution equation with a spectral operator of scalar type |
| title_short | On an abstract evolution equation with a spectral operator of scalar type |
| title_sort | on an abstract evolution equation with a spectral operator of scalar type |
| url | http://dx.doi.org/10.1155/S0161171202112233 |
| work_keys_str_mv | AT maratvmarkin onanabstractevolutionequationwithaspectraloperatorofscalartype |