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The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories. Many problems are studied in the nilpotent case, but several obstacles arise when encompassing exponentially solvable settings. The book offers the most recent solutions to a number of open questions that arose over the last decades, presents the newest related results, and offers an alluring platform for progressing in this research area. The book is unique in the literature for which the readership extends to graduate students, researchers, and beginners in the fields of harmonic analysis on solvable homogeneous spaces.
1. Branching Laws and the Multiplicity Function of Unitary Representations of Exponential Solvable Lie Groups. - 2. Intertwining Operators for Irreducible Representations of an Exponential Solvable Lie Group. - 3. Intertwining Operators of Induced Representations and Restrictions of Representations of Exponential Solvable Lie Groups. - 4. Variants of Plancherel Formulas for Monomial Representations of Exponential Solvable Lie Groups. - 5. Polynomial Conjectures. - 6. Holomorphically Induced Representations of Solvable Lie Groups. - 7. Monomial Representations of Discrete Type of Exponential Solvable Lie Groups. - 8. Bounded Irreducible Representations.
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The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories. Many problems are studied in the nilpotent case, but several obstacles arise when encompassing exponentially solvable settings. The book offers the most recent solutions to a number of open questions that arose over the last decades, presents the newest related results, and offers an alluring platform for progressing in this research area. The book is unique in the literature for which the readership extends to graduate students, researchers, and beginners in the fields of harmonic analysis on solvable homogeneous spaces.
