Harmonic Functions And Potentials On Finite Or Infinite Networks
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Harmonic Functions And Potentials On Finite Or Infinite Networks
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Author : Victor Anandam
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Harmonic Functions And Potentials On Finite Or Infinite Networks written by Victor Anandam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-27 with Mathematics categories.
Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.
Potential Theory On Infinite Networks
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Author : Paolo M. Soardi
language : en
Publisher: Springer
Release Date : 2006-11-15
Potential Theory On Infinite Networks written by Paolo M. Soardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.
Frontiers In Analysis And Probability
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Author : Nalini Anantharaman
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Frontiers In Analysis And Probability written by Nalini Anantharaman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.
Complex Analysis And Potential Theory
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Author : Andre Boivin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Complex Analysis And Potential Theory written by Andre Boivin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.
Inverse Problems Regularization Methods And Related Topics
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Author : Sergei V. Pereverzyev
language : en
Publisher: Springer Nature
Release Date : 2025-03-31
Inverse Problems Regularization Methods And Related Topics written by Sergei V. Pereverzyev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-31 with Mathematics categories.
This book features a thoughtfully curated collection of research contributions spanning regularization theory, integral equations, learning theory, and matrix and operator theory. These contributions were presented in honor of Prof. M. Thamban Nair on his 65th birthday during the International Conference on Analysis, Inverse Problems, and Applications, which took place at the IIT Madras in Chennai, India, from July 18–21, 2022. The book is a valuable resource for graduate students, engineers, scientists, and researchers looking to advance their work in the development of innovative regularization algorithms. It comprises 14 chapters contributed by esteemed experts and emerging researchers.
Operator Theory And Analysis Of Infinite Networks
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Author : Palle Jorgensen
language : en
Publisher: World Scientific
Release Date : 2023-03-21
Operator Theory And Analysis Of Infinite Networks written by Palle Jorgensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-21 with Mathematics categories.
This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.
Random Walks And Discrete Potential Theory
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Author : M. Picardello
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18
Random Walks And Discrete Potential Theory written by M. Picardello and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-18 with Mathematics categories.
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Algebra Graph Theory And Their Applications
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Author : T.T Chelvam
language : en
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
Release Date : 2009-12-03
Algebra Graph Theory And Their Applications written by T.T Chelvam and has been published by ALPHA SCIENCE INTERNATIONAL LIMITED this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-03 with Mathematics categories.
Algebra and Graph Theory are two fascinating branches of Mathematics. The tools of each have been used in the other to explore and investigate problems in depth. Especially the Cayley graphs constructed out of the group structures have been greatly and extensively used in Parallel computers to provide network to the routing problem. ALGEBRA, GRAPH THEORY AND THEIR APPLICATIONS takes an inclusive view of the two areas and presents a wide range of topics. It includes sixteen referred research articles on algebra and graph theory of which three are expository in nature alongwith articles exhibiting the use of algebraic techniques in the study of graphs. A substantial proportion of the book covers topics that have not yet appeared in book form providing a useful resource to the younger generation of researchers in Discrete Mathematics.
Hokkaido Mathematical Journal
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Author :
language : en
Publisher:
Release Date : 2015
Hokkaido Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
Random Walks And Heat Kernels On Graphs
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Author : M. T. Barlow
language : en
Publisher: Cambridge University Press
Release Date : 2017-02-23
Random Walks And Heat Kernels On Graphs written by M. T. Barlow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-23 with Mathematics categories.
Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.