书目名称 | Harmonic Analysis on Exponential Solvable Lie Groups |
编辑 | Hidenori Fujiwara,Jean Ludwig |
视频video | http://file.papertrans.cn/425/424279/424279.mp4 |
概述 | Explains topics that have been actively studied in the non-commutative harmonic analysis of solvable Lie groups.Gives the classical standard results with proof related to the so-called orbit method.Pr |
丛书名称 | Springer Monographs in Mathematics |
图书封面 |  |
描述 | .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, Frobeniusreciprocity, and associated algebras of invariant differential operators..The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a deta |
出版日期 | Book 2015 |
关键词 | Exponential solvable Lie group; Induced representation; Nilpotent Lie group; Orbit method; Restriction o |
版次 | 1 |
doi | https://doi.org/10.1007/978-4-431-55288-8 |
isbn_softcover | 978-4-431-56390-7 |
isbn_ebook | 978-4-431-55288-8Series ISSN 1439-7382 Series E-ISSN 2196-9922 |
issn_series | 1439-7382 |
copyright | Springer Japan 2015 |