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Harmonic Analysis on Exponential Solvable Lie Groups

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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.

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Series Title

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Call Number

300 FUJ h

Publisher

: ., 2015

Collation

XI, 465

Language

English

ISBN/ISSN

978-4-431-55287-1

Classification

300

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

Topological Groups

Specific Detail Info

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Statement of Responsibility

Hidenori Fujiwara , Jean Ludwig

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Khusnun

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