A note on the spectral operators of scalar type and semigroups of bounded linear operators
It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0- and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator bein...
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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/S0161171202112221 |
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| _version_ | 1850162990805942272 |
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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, for the spectral operators of scalar type, the well-known characterizations of the generation of C0- and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator. |
| format | Article |
| id | doaj-art-ef4e24e8e4934c48a3e731023210f896 |
| 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-ef4e24e8e4934c48a3e731023210f8962025-08-20T02:22:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01321063564010.1155/S0161171202112221A note on the spectral operators of scalar type and semigroups of bounded linear operatorsMarat V. Markin0Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston 02215, MA, USAIt is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0- and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.http://dx.doi.org/10.1155/S0161171202112221 |
| spellingShingle | Marat V. Markin A note on the spectral operators of scalar type and semigroups of bounded linear operators International Journal of Mathematics and Mathematical Sciences |
| title | A note on the spectral operators of scalar type and semigroups of bounded linear
operators |
| title_full | A note on the spectral operators of scalar type and semigroups of bounded linear
operators |
| title_fullStr | A note on the spectral operators of scalar type and semigroups of bounded linear
operators |
| title_full_unstemmed | A note on the spectral operators of scalar type and semigroups of bounded linear
operators |
| title_short | A note on the spectral operators of scalar type and semigroups of bounded linear
operators |
| title_sort | note on the spectral operators of scalar type and semigroups of bounded linear operators |
| url | http://dx.doi.org/10.1155/S0161171202112221 |
| work_keys_str_mv | AT maratvmarkin anoteonthespectraloperatorsofscalartypeandsemigroupsofboundedlinearoperators AT maratvmarkin noteonthespectraloperatorsofscalartypeandsemigroupsofboundedlinearoperators |