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# đź“™ Lie Theory: Harmonic Analysis on Symmetric Spacesâ€”General Plancherel Theorems by Erik P. van den Ban (auth.), Jean-Philippe Anker, Bent Orsted (eds.) â€” free pdf

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Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title *Lie Theory*, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory.

*Harmonic Analysis on Symmetric Spacesâ€”General Plancherel Theorems* presents extensive surveys by **E.P. van den Ban**, **H. Schlichtkrull**, and **P. Delorme** of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces.

Van den Banâ€™s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maassâ€“Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paleyâ€“Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.

Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, *Harmonic Analysis on Symmetric Spacesâ€”General Plancherel Theorems* provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required.

- Series:
**Progress in Mathematics 230** - Author:
**Erik P. van den Ban (auth.), Jean-Philippe Anker, Bent Orsted (eds.)** - Year:
**2005** - Publisher:
**BirkhĂ¤user Basel** - Language:
**English** - ISBN:
**9780817637774,0-8176-3777-X**

- File size:
**1 220 501** - Format:
**pdf**

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Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis,Â and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature su...

* Presents extensive surveys by van den Ban, Schlichtkrull, and Delorme of the recentÂ progress in deriving the Plancherel theorem on reductive symmetric spaces * Well suited for both graduate students and researchers in semisimple Lie theory and neighb...

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers...

During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions. The technique has had several important applications in harmonic analysis for symme...

This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the PoincarĂ© upper half plane.Â This book is intended for beginning graduate students in mathematics or researchers in physi...

[...].Symmetric spaces are hugely important objects, occurring in many different parts of contemporary mathematics. In number theory, for example, one cannot even begin to do modular forms seriously without a reasonably thorough knowledge of the symmetri...

The two parts of this sharply focused book, Hypergeometric and Special Functions and Harmonic Analysis on Semisimple Symmetric Spaces, are derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent d...

The two parts of this sharply focused book, Hypergeometric and Special Functions and Harmonic Analysis on Semisimple Symmetric Spaces, are derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent d...

The two parts of this sharply focused book, Hypergeometric and Special Functions and Harmonic Analysis on Semisimple Symmetric Spaces, are derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent d...