Name: Unitary Representations and Unitary Duals
SKU: 64791329
Price: 83.67 USD
Availability: InStock
Author: Manfred Einsiedler;Thomas Ward
ISBN: 9783032038982

portada Unitary Representations and Unitary Duals

Unitary Representations and Unitary Duals

Formato

Libro Físico

Editorial

Springer Nature Switzerland AG

Autor

Manfred Einsiedler;Thomas Ward

Colección

Graduate Texts in Mathematics

Año

2025

N° páginas

559

Encuadernación

Tapa Dura

Dimensiones

23.5x15.5 cm

ISBN13

9783032038982

Unitary Representations and Unitary Duals

Manfred Einsiedler;Thomas Ward (Autor) · Springer Nature Switzerland AG · Tapa Dura

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Reseña del libro "Unitary Representations and Unitary Duals"

This graduate textbook introduces the unitary representation theory of groups, emphasizing applications in fields like dynamical systems. It begins with the general theory and motivation, then explores key classes of groups. Abelian and compact groups are treated through Pontryagin duality and the Peter–Weyl theorem. Metabelian groups illustrate links to ergodic theory and lead to the Mackey machine. Weak containment and the Fell topology are introduced through examples. The final chapters apply the theory to special linear groups in dimensions two and three, covering smooth vectors, spectral gaps, and decay of matrix coefficients. The two-dimensional case is examined in depth, including the Kunze–Stein phenomenon, spectral decomposition on the hyperbolic plane, and the Weil representation. The book concludes with a full description of the unitary dual of SL(2,R) and its Fell topology, applying the theory to prove effective equidistribution of horocycle orbits. With its focus on key examples and concrete explanations, this textbook is aimed at graduate students taking first steps in unitary representation theory. It builds the theory from the ground up, requiring only some familiarity with functional analysis beyond standard undergraduate mathematics.