This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
This article has been tagged as part of a large-scale clean-up project of multiple article copyright infringement. (See the investigation subpage) It will likely be deleted after one week unless it can be verified to be free of infringement. For legal reasons, Wikipedia cannot accept copyrighted text or images borrowed from other web sites or printed material; such additions must be deleted. Major contributions by contributors who have been verified to have violated copyright in multiple articles may be presumptively deleted in accordance with Wikipedia:Copyright violations.
Interested contributors are invited to help clarify the copyright status of this material or rewriting the article in original language at the temporary page linked from the article's face. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. -- r.e.b. ( talk) 02:22, 22 December 2009 (UTC)
After rebuilding this article the article GJMS operator should be merged with this one as it is just a generalization. franklin 15:37, 22 December 2009 (UTC)
Yes, GJMS operators are substantially different from the Paneitz operators. In particular, the GJMS operators are naturally thought of as a hierarchy of differential operators coming from the ambient construction. While the Paneitz operators are in fact special cases, much more analysis has been done on them (e.g., positivity, eigenvalue problems, etc.) that a separate article could exist discussing these. The GJMS operators, particular the so-called "critical" GJMS operators, in turn are vital in the definition of the obstruction tensor and Q-curvature. So while one thing is a special case of the other, the two things are analyzed from completely different points of view, and have often very different kinds of results associated with them. Are you convinced? Sławomir Biały ( talk) 16:49, 22 December 2009 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
This article has been tagged as part of a large-scale clean-up project of multiple article copyright infringement. (See the investigation subpage) It will likely be deleted after one week unless it can be verified to be free of infringement. For legal reasons, Wikipedia cannot accept copyrighted text or images borrowed from other web sites or printed material; such additions must be deleted. Major contributions by contributors who have been verified to have violated copyright in multiple articles may be presumptively deleted in accordance with Wikipedia:Copyright violations.
Interested contributors are invited to help clarify the copyright status of this material or rewriting the article in original language at the temporary page linked from the article's face. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. -- r.e.b. ( talk) 02:22, 22 December 2009 (UTC)
After rebuilding this article the article GJMS operator should be merged with this one as it is just a generalization. franklin 15:37, 22 December 2009 (UTC)
Yes, GJMS operators are substantially different from the Paneitz operators. In particular, the GJMS operators are naturally thought of as a hierarchy of differential operators coming from the ambient construction. While the Paneitz operators are in fact special cases, much more analysis has been done on them (e.g., positivity, eigenvalue problems, etc.) that a separate article could exist discussing these. The GJMS operators, particular the so-called "critical" GJMS operators, in turn are vital in the definition of the obstruction tensor and Q-curvature. So while one thing is a special case of the other, the two things are analyzed from completely different points of view, and have often very different kinds of results associated with them. Are you convinced? Sławomir Biały ( talk) 16:49, 22 December 2009 (UTC)