On weighted positivity of ordinary differential operators
<p/> <p>Some elliptic differential operators possess a weighted positivity property, where the weight is a fundamental solution of the operator. This property has interesting applications to partial differential operators. The present paper is devoted to the property for ordinarydifferen...
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| Format: | Article |
| Language: | English |
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SpringerOpen
1999-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/4/791607 |
| Summary: | <p/> <p>Some elliptic differential operators possess a weighted positivity property, where the weight is a fundamental solution of the operator. This property has interesting applications to partial differential operators. The present paper is devoted to the property for ordinarydifferential operators.</p> <p>It is shown that the operator <inline-formula><graphic file="1029-242X-1999-791607-i1.gif"/></inline-formula> has the positivity property if and only if <inline-formula><graphic file="1029-242X-1999-791607-i2.gif"/></inline-formula>, while there exist operators of arbitrary even order for which the positivity holds. Some necessary conditions for the property are given.</p> |
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| ISSN: | 1025-5834 1029-242X |