Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Organization of the Book
- Part I Basics: Foundational Material, Elementary Aspects, and Examples
- 1 Introduction
- 2 The Abstract Setting
- 3 The Classical Case: Eigenvalues on Euclidean Domains and Riemannian Manifold
- 4 First Properties of the Spectrum
- 5 Eigenvalues and Eigenfunctions of the Laplace Operator via Floer Theory
- Part II Eigenvalues and Eigenfunctions on Simplicial Complexes and Hypergraphs
- Part III Additional Topics: Interlacing, Tensors, Nonbacktracking Laplacians, and Applications
- Remarks on Notation
- References
- Index
1 - Introduction
from Part I - Basics: Foundational Material, Elementary Aspects, and Examples
Published online by Cambridge University Press: 21 May 2026
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Organization of the Book
- Part I Basics: Foundational Material, Elementary Aspects, and Examples
- 1 Introduction
- 2 The Abstract Setting
- 3 The Classical Case: Eigenvalues on Euclidean Domains and Riemannian Manifold
- 4 First Properties of the Spectrum
- 5 Eigenvalues and Eigenfunctions of the Laplace Operator via Floer Theory
- Part II Eigenvalues and Eigenfunctions on Simplicial Complexes and Hypergraphs
- Part III Additional Topics: Interlacing, Tensors, Nonbacktracking Laplacians, and Applications
- Remarks on Notation
- References
- Index
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Summary
This chapter provides a historical introduction. Spectra first appeared in the study of linear differential operators, such as the Laplace, the heat, and the wave operator, which originated in the eighteenth century. A Laplace operator on networks was first introduced by Kirchhoff in the ninteenth century.
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- Spectra of Discrete Structures , pp. 3 - 13Publisher: Cambridge University PressPrint publication year: 2026
- Creative Commons
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC 4.0 https://creativecommons.org/cclicenses/
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