Graphs And Discrete Dirichlet Spaces PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Graphs And Discrete Dirichlet Spaces PDF full book. Access full book title Graphs And Discrete Dirichlet Spaces.
Author | : Matthias Keller |
Publisher | : Springer Nature |
Total Pages | : 675 |
Release | : 2021-10-22 |
Genre | : Mathematics |
ISBN | : 3030814599 |
Download Graphs and Discrete Dirichlet Spaces Book in PDF, ePub and Kindle
The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Author | : Matthias Keller |
Publisher | : |
Total Pages | : 0 |
Release | : 2021 |
Genre | : |
ISBN | : 9783030814601 |
Download Graphs and Discrete Dirichlet Spaces Book in PDF, ePub and Kindle
The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Author | : José M. Mazón |
Publisher | : Springer Nature |
Total Pages | : 396 |
Release | : 2023-08-04 |
Genre | : Mathematics |
ISBN | : 3031335848 |
Download Variational and Diffusion Problems in Random Walk Spaces Book in PDF, ePub and Kindle
This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research. Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.
Author | : Matthias Keller |
Publisher | : Cambridge University Press |
Total Pages | : 493 |
Release | : 2020-08-20 |
Genre | : Mathematics |
ISBN | : 1108587380 |
Download Analysis and Geometry on Graphs and Manifolds Book in PDF, ePub and Kindle
This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
Author | : Luca Calatroni |
Publisher | : Springer Nature |
Total Pages | : 767 |
Release | : 2023-05-09 |
Genre | : Computers |
ISBN | : 3031319753 |
Download Scale Space and Variational Methods in Computer Vision Book in PDF, ePub and Kindle
This book constitutes the proceedings of the 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, which took place in Santa Margherita di Pula, Italy, in May 2023. The 57 papers presented in this volume were carefully reviewed and selected from 72 submissions. They were organized in topical sections as follows: Inverse Problems in Imaging; Machine and Deep Learning in Imaging; Optimization for Imaging: Theory and Methods; Scale Space, PDEs, Flow, Motion and Registration.
Author | : Olaf Post |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2012-01-06 |
Genre | : Mathematics |
ISBN | : 3642238394 |
Download Spectral Analysis on Graph-like Spaces Book in PDF, ePub and Kindle
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
Author | : Nicola Arcozzi |
Publisher | : American Mathematical Soc. |
Total Pages | : 536 |
Release | : 2019-09-03 |
Genre | : Dirichlet principle |
ISBN | : 1470450828 |
Download The Dirichlet Space and Related Function Spaces Book in PDF, ePub and Kindle
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Author | : Rick Durrett |
Publisher | : Cambridge University Press |
Total Pages | : 203 |
Release | : 2010-05-31 |
Genre | : Mathematics |
ISBN | : 1139460889 |
Download Random Graph Dynamics Book in PDF, ePub and Kindle
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author | : Omar El-Fallah |
Publisher | : Cambridge University Press |
Total Pages | : 227 |
Release | : 2014-01-16 |
Genre | : Mathematics |
ISBN | : 1107047528 |
Download A Primer on the Dirichlet Space Book in PDF, ePub and Kindle
The first systematic account of the Dirichlet space, one of the most fundamental Hilbert spaces of analytic functions.
Author | : Russell Lyons |
Publisher | : Cambridge University Press |
Total Pages | : 1106 |
Release | : 2017-01-20 |
Genre | : Mathematics |
ISBN | : 1316785335 |
Download Probability on Trees and Networks Book in PDF, ePub and Kindle
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.