國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Harmonic analysis on exponential sol...

Fujiwara, Hidenori.

Harmonic analysis on exponential solvable lie groups

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Harmonic analysis on exponential solvable lie groupsby Hidenori Fujiwara, Jean Ludwig.
作者:	Fujiwara, Hidenori.
其他作者:	Ludwig, Jean.
出版者:	Tokyo :Springer Japan :2015.
面頁冊數:	xi, 465 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Harmonic analysis.
電子資源:	http://dx.doi.org/10.1007/978-4-431-55288-8
ISBN:	9784431552888 (electronic bk.)

Harmonic analysis on exponential solvable lie groups
Fujiwara, Hidenori.

Harmonic analysis on exponential solvable lie groups[electronic resource] /by Hidenori Fujiwara, Jean Ludwig. - Tokyo :Springer Japan :2015. - xi, 465 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that the group is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.

ISBN: 9784431552888 (electronic bk.)

Standard No.: 10.1007/978-4-431-55288-8doiSubjects--Topical Terms:

189705
Harmonic analysis.

LC Class. No.: QA403

Dewey Class. No.: 515.2433

Harmonic analysis on exponential solvable lie groups
LDR:02886nmm a2200325 a 4500 001 461175
003 DE-He213
005 20150812140443.0
006 m d
007 cr nn 008maaau
008 151110s2015 ja s 0 eng d
020 $a 9784431552888 (electronic bk.)
020 $a 9784431552871 (paper)
024 7 $a 10.1007/978-4-431-55288-8 $2 doi
035 $a 978-4-431-55288-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA403
072 7 $a PBG $2 bicssc
072 7 $a MAT014000 $2 bisacsh
072 7 $a MAT038000 $2 bisacsh
082 0 4 $a 515.2433 $2 23
090 $a QA403 $b .F961 2015
100 1 $a Fujiwara, Hidenori. $3 713103
245 1 0 $a Harmonic analysis on exponential solvable lie groups $h [electronic resource] / $c by Hidenori Fujiwara, Jean Ludwig.
260 $a Tokyo : $b Springer Japan : $b Imprint: Springer, $c 2015.
300 $a xi, 465 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
520 $a 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. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that the group is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.
650 0 $a Harmonic analysis. $3 189705
650 0 $a Lie groups. $3 190898
650 0 $a Lie algebras. $3 191078
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Topological Groups, Lie Groups. $3 273787
650 2 4 $a Abstract Harmonic Analysis. $3 274074
650 2 4 $a Functional Analysis. $3 274845
700 1 $a Ludwig, Jean. $3 713104
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u http://dx.doi.org/10.1007/978-4-431-55288-8
950 $a Mathematics and Statistics (Springer-11649)