Harmonic Analysis on Exponential Solvable Lie Groups
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivat...
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Springer
2015
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oai:scholar.dlu.edu.vn:DLU123456789-584502023-11-11T06:07:39Z Harmonic Analysis on Exponential Solvable Lie Groups Fujiwara, Hidenori Ludwig, Jean Harmonic analysis Lie groups Lie algebras This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. 2015-09-23T02:51:14Z 2015-09-23T02:51:14Z 2015 Book 978-4-431-55288-8 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58450 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Harmonic analysis Lie groups Lie algebras |
| spellingShingle |
Harmonic analysis Lie groups Lie algebras Fujiwara, Hidenori Ludwig, Jean Harmonic Analysis on Exponential Solvable Lie Groups |
| description |
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers.
The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. |
| format |
Book |
| author |
Fujiwara, Hidenori Ludwig, Jean |
| author_facet |
Fujiwara, Hidenori Ludwig, Jean |
| author_sort |
Fujiwara, Hidenori |
| title |
Harmonic Analysis on Exponential Solvable Lie Groups |
| title_short |
Harmonic Analysis on Exponential Solvable Lie Groups |
| title_full |
Harmonic Analysis on Exponential Solvable Lie Groups |
| title_fullStr |
Harmonic Analysis on Exponential Solvable Lie Groups |
| title_full_unstemmed |
Harmonic Analysis on Exponential Solvable Lie Groups |
| title_sort |
harmonic analysis on exponential solvable lie groups |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58450 |
| _version_ |
1819777586352357376 |