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.

Autorentext

Ali Baklouti is a Full Professor of Mathematics at the University of Sfax, Tunisia. He received his Ph.D. in Mathematics from the University of Metz (France) in 1995. He was elected as Vice-President of the University of Sfax since December 2020 and as the President of the Tunisian Mathematical Society for two consecutive terms (April 2016March 2019 and April 2019March 2022), and he has been the Deputy Director of the Mediterranean Institute of Mathematical Sciences since January 2012. He was also nominated as a member of the Tunisian Academy of Sciences, Letters and Arts: Beit Elhikma in December 2016. He published over 80 papers in peer-reviewed international journals and proceedings, as well as many book chapters. He is Co-Editor-in-Chief of the Tunisian Journal of Mathematics and Advances in Pure and Applied Mathematics.

Hidenori Fujiwara is an Emeritus Professor of Kinki University, Japan. He had been a Full Professor of Kinki University for 26 years and retired in 2013. He received his Ph.D. in Mathematics from Tokyo University (Japan) in1977. He studies the unitary representations of solvable Lie groups and the harmonic analysis on solvable homogeneous spaces. He published over 40 papers in peer-reviewed international journals, as well as two books.

Jean Ludwig is currently Professeur émérite at the Université de Lorraine, France. He received his Ph.D. in Mathematics from the University of Bielefeld (Germany) in 1976 and his habilitation in 1979. He was a professor of Metz University (France) from 1990 to 2014. He had 13 PHD students, and he published over 100 papers in peer-reviewed international journals and proceedings and acted as a co-editor of the Journal of Lie Theory. He had been Directeur du Labaoratoire LMAM for 3 years and had many administrative duties at the Department and UFR level at the University of Bielefeld and Metz.

Inhalt

• 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.