Harmonic Functions and Potentials on Finite or Infinite Networks [recurso electrónico] / by Victor Anandam.
Tipo de material: TextoSeries Lecture Notes of the Unione Matematica Italiana ; 12Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: X, 141p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642213991Tema(s): Mathematics | Functions of complex variables | Differential equations, partial | Potential theory (Mathematics) | Mathematics | Potential Theory | Functions of a Complex Variable | Partial Differential EquationsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515.96 Clasificación LoC:QA404.7-405Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA404.7 -405 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 376267-2001 |
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QA403.5 -404.5 Discrete Fourier Analysis | QA403.5 -404.5 Morrey and Campanato Meet Besov, Lizorkin and Triebel | QA404.7 -405 Potential Theory | QA404.7 -405 Harmonic Functions and Potentials on Finite or Infinite Networks | QA431 Integral Methods in Science and Engineering, Volume 2 | QA431 Integral Methods in Science and Engineering, Volume 1 | QA431 Integral Methods in Science and Engineering |
1 Laplace Operators on Networks and Trees -- 2 Potential Theory on Finite Networks -- 3 Harmonic Function Theory on Infinite Networks -- 4 Schrödinger Operators and Subordinate Structures on Infinite Networks -- 5 Polyharmonic Functions on Trees.
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.
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