Groups and Analysis: The Legacy of Hermann Weyl

doi:10.1017/CBO9780511721410

Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as well as foundations of mathematics. In this volume, leading experts present his lasting influence on current mathematics, often connecting Weyl's theorems with cutting edge research in dynamical systems, invariant theory, and partial differential equations. In a broad and accessible presentation, survey chapters describe the historical development of each area alongside up-to-the-minute results, focussing on the mathematical roots evident within Weyl's work.

'The quality of the articles is high: the promise of the title is met, and the material is presented at a very accessible level, but without courting triviality. … uncommonly informative and fascinating …'

Source: MAA Reviews

'… offers an interesting overview of the impact of H. Weyl's work on contemporary mathematics.'

Source: EMS Newsletter

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-ix
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List of speakers and talks
pp x-x
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1 - Harmonic analysis on compact symmetric spaces
pp 1-23
- By Roe Goodman, Department of Mathematics Rutgers, The State University of New Jersey
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2 - Weyl, eigenfunction expansions, symmetric spaces
pp 24-62
- By Erik van den Ban, University of Utrecht
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3 - Weyl's work on singular Sturm–Liouville operators
pp 63-83
- By W.N. Everitt, School of Mathematics and Statistics University of Birmingham, H. Kalf, Mathematisches Institut Universität München
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4 - From Weyl quantization to modern algebraic index theory
pp 84-99
- By Markus J. Pflaum, Fachbereich Mathematik Goethe-Universität Frankfurt/Main
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5 - Sharp spectral inequalities for the Heisenberg Laplacian
pp 100-115
- By A.M. Hansson, Department of Mathematics, KTH, A. Laptev, Department of Mathematics Imperial College, London
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6 - Equidistribution for quadratic differentials
pp 116-132
- By Ursula Hamenstädt, Mathematisches Institut Rheinische Friedrich-Wilhelms-Universität Bonn
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7 - Weyl's law in the theory of automorphic forms
pp 133-163
- By Werner Müller, Universität Bonn Mathematisches Institut
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8 - Weyl's Lemma, one of many
pp 164-173
- By Daniel W. Stroock, M.I.T., 2-272, Cambridge, MA 02140, U.S.A.
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9 - Analysis on foliated spaces and arithmetic geometry
pp 174-190
- By Christopher Deninger, Mathematisches Institut Einsteinstr. 62 48149 Münster, Germany
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10 - Reciprocity algebras and branching
pp 191-231
- By Roger E. Howe, Department of Mathematics, Yale University, Eng-Chye Tan, Department of Mathematics, National University of Singapore, Jeb F. Willenbring, Department of Mathematical Sciences, University of Wisconsin at Milwaukee
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11 - Character formulae from Hermann Weyl to the present
pp 232-270
- By Jens Carsten Jantzen, Mathematics Institute Aarhus Universitet
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12 - The Classification of affine buildings
pp 271-284
- By Richard M. Weiss, Department of Mathematics Tufts University
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13 - Emmy Noether and Hermann Weyl
pp 285-326
- By Peter Roquette, Mathematisches Institut, Universität Heidelberg
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Groups and Analysis

The Legacy of Hermann Weyl

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-ix

List of speakers and talks
pp x-x

1 - Harmonic analysis on compact symmetric spaces
pp 1-23

2 - Weyl, eigenfunction expansions, symmetric spaces
pp 24-62

3 - Weyl's work on singular Sturm–Liouville operators
pp 63-83

4 - From Weyl quantization to modern algebraic index theory
pp 84-99

5 - Sharp spectral inequalities for the Heisenberg Laplacian
pp 100-115

6 - Equidistribution for quadratic differentials
pp 116-132

7 - Weyl's law in the theory of automorphic forms
pp 133-163

8 - Weyl's Lemma, one of many
pp 164-173

9 - Analysis on foliated spaces and arithmetic geometry
pp 174-190

10 - Reciprocity algebras and branching
pp 191-231

11 - Character formulae from Hermann Weyl to the present
pp 232-270

12 - The Classification of affine buildings
pp 271-284

13 - Emmy Noether and Hermann Weyl
pp 285-326

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Groups and Analysis

The Legacy of Hermann Weyl

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