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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Harmonic Analysis on Exponential Solvable Lie Groups
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Harmonic Analysis on Exponential Solvable Lie Groups
Hidenori Fujiwara (Gebundene Ausgabe, Englisch)
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Beschreibung
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 detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that
G
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
16.12.2014
Sprache
Englisch
EAN
9784431552871
Herausgeber
Springer Tokyo
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Hidenori Fujiwara
Seitenanzahl
465
Auflage
1
Einbandart
Gebundene Ausgabe
Schlagwörter
Exponential solvable Lie group, Induced representation, Nilpotent Lie group, Orbit method, Restriction of representation
Thema-Inhalt
PBG - Gruppen und Gruppentheorie
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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