A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in ord…
Introduction to analysis on graphs
A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in ord…
Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a…
Cover; Title; Copyright; Contents; Introduction; 1 The Laplacian on aRiemannian Manifold; 1.1 Basic Examples; 1.1.1 The Laplacian on S1 and R; 1.1.2 Heat Flow on S1 and R; 1.2 The Laplacian on a Riemannian Manifold; 1.2.1 Riemannian Metrics; 1.2.2 L2 Spaces of Functions and Form…
This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatmen…
