Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem
A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its co...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-12-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0033/spma-2016-0033.xml?format=INT |
| _version_ | 1818912842254909440 |
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| author | Tam Tin-Yau Hill William C. |
| author_facet | Tam Tin-Yau Hill William C. |
| author_sort | Tam Tin-Yau |
| collection | DOAJ |
| description | A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The
generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis.
The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also
discuss the derivatives of some orbital functions. |
| first_indexed | 2024-12-19T23:21:01Z |
| format | Article |
| id | doaj.art-40adcbe6efdf4b60bce9acdda8348fe3 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-19T23:21:01Z |
| publishDate | 2016-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-40adcbe6efdf4b60bce9acdda8348fe32022-12-21T20:01:58ZengDe GruyterSpecial Matrices2300-74512016-12-014110.1515/spma-2016-0033spma-2016-0033Derivatives of orbital function and an extension of Berezin-Gel’fand’s theoremTam Tin-Yau0Hill William C.1Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, AL 36849-5310, USADepartment of Mathematics, Middle Georgia State University, 100 University Pkwy, Macon, GA 31206, USAA generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also discuss the derivatives of some orbital functions.http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0033/spma-2016-0033.xml?format=INTBerezin-Gel’fand’s theorem subdifferential Clarke generalized gradient Lebourg mean value theorem Eaton triple reduced triple finite reflection group |
| spellingShingle | Tam Tin-Yau Hill William C. Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem Special Matrices Berezin-Gel’fand’s theorem subdifferential Clarke generalized gradient Lebourg mean value theorem Eaton triple reduced triple finite reflection group |
| title | Derivatives of orbital function and an
extension of Berezin-Gel’fand’s theorem |
| title_full | Derivatives of orbital function and an
extension of Berezin-Gel’fand’s theorem |
| title_fullStr | Derivatives of orbital function and an
extension of Berezin-Gel’fand’s theorem |
| title_full_unstemmed | Derivatives of orbital function and an
extension of Berezin-Gel’fand’s theorem |
| title_short | Derivatives of orbital function and an
extension of Berezin-Gel’fand’s theorem |
| title_sort | derivatives of orbital function and an extension of berezin gel fand s theorem |
| topic | Berezin-Gel’fand’s theorem subdifferential Clarke generalized gradient Lebourg mean value theorem Eaton triple reduced triple finite reflection group |
| url | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0033/spma-2016-0033.xml?format=INT |
| work_keys_str_mv | AT tamtinyau derivativesoforbitalfunctionandanextensionofberezingelfandstheorem AT hillwilliamc derivativesoforbitalfunctionandanextensionofberezingelfandstheorem |