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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SpringerOpen
1999-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://www.journalofinequalitiesandapplications.com/content/4/791607 |
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doaj-9c22b8ad4f934cacaddb4971b49c3b472020-11-24T20:48:01ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1999-01-0119994791607On weighted positivity of ordinary differential operatorsEilertsen Stefan<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>http://www.journalofinequalitiesandapplications.com/content/4/791607Integral inequalitiesDifferential operatorsIntegral operators |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Eilertsen Stefan |
| spellingShingle |
Eilertsen Stefan On weighted positivity of ordinary differential operators Journal of Inequalities and Applications Integral inequalities Differential operators Integral operators |
| author_facet |
Eilertsen Stefan |
| author_sort |
Eilertsen Stefan |
| title |
On weighted positivity of ordinary differential operators |
| title_short |
On weighted positivity of ordinary differential operators |
| title_full |
On weighted positivity of ordinary differential operators |
| title_fullStr |
On weighted positivity of ordinary differential operators |
| title_full_unstemmed |
On weighted positivity of ordinary differential operators |
| title_sort |
on weighted positivity of ordinary differential operators |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
1999-01-01 |
| description |
<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> |
| topic |
Integral inequalities Differential operators Integral operators |
| url |
http://www.journalofinequalitiesandapplications.com/content/4/791607 |
| work_keys_str_mv |
AT eilertsenstefan onweightedpositivityofordinarydifferentialoperators |
| _version_ |
1716809170660884480 |