Schwartz analysis and intertwining distributions
In this dissertation, we combine the work of A. Aizenbud and D. Gourevitch on Schwartz functions on Nash manifolds, and the work of F. du Cloux on Schwartz inductions, to develop a toolbox of Schwartz analysis. We then use these tools to study the intertwining operators between parabolic inductions,...
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University of British Columbia
2017
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| Online Access: | http://hdl.handle.net/2429/64171 |
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ndltd-UBC-oai-circle.library.ubc.ca-2429-641712018-01-05T17:30:15Z Schwartz analysis and intertwining distributions Liu, Xinyu In this dissertation, we combine the work of A. Aizenbud and D. Gourevitch on Schwartz functions on Nash manifolds, and the work of F. du Cloux on Schwartz inductions, to develop a toolbox of Schwartz analysis. We then use these tools to study the intertwining operators between parabolic inductions, and study the behavior of intertwining distributions on certain open subsets. Finally we use our results to give new proof of results in Bruhat's thesis on irreducibilities of degenerate principal series and minimal principal series. Science, Faculty of Mathematics, Department of Graduate 2017-12-22T23:30:15Z 2017-12-22T23:30:15Z 2017 2018-02 Text Thesis/Dissertation http://hdl.handle.net/2429/64171 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ University of British Columbia |
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NDLTD |
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English |
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NDLTD |
| description |
In this dissertation, we combine the work of A. Aizenbud and D. Gourevitch on Schwartz functions on Nash manifolds, and the work of F. du Cloux on Schwartz inductions, to develop a toolbox of Schwartz analysis. We then use these tools to study the intertwining operators between parabolic inductions, and study the behavior of intertwining distributions on certain open subsets. Finally we use our results to give new proof of results in Bruhat's thesis on irreducibilities of degenerate principal series and minimal principal series. === Science, Faculty of === Mathematics, Department of === Graduate |
| author |
Liu, Xinyu |
| spellingShingle |
Liu, Xinyu Schwartz analysis and intertwining distributions |
| author_facet |
Liu, Xinyu |
| author_sort |
Liu, Xinyu |
| title |
Schwartz analysis and intertwining distributions |
| title_short |
Schwartz analysis and intertwining distributions |
| title_full |
Schwartz analysis and intertwining distributions |
| title_fullStr |
Schwartz analysis and intertwining distributions |
| title_full_unstemmed |
Schwartz analysis and intertwining distributions |
| title_sort |
schwartz analysis and intertwining distributions |
| publisher |
University of British Columbia |
| publishDate |
2017 |
| url |
http://hdl.handle.net/2429/64171 |
| work_keys_str_mv |
AT liuxinyu schwartzanalysisandintertwiningdistributions |
| _version_ |
1718586063805480960 |