Anandam, Victor.
Harmonic Functions and Potentials on Finite or Infinite Networks [electronic resource] / by Victor Anandam. - X, 141p. online resource. - Lecture Notes of the Unione Matematica Italiana, 12 1862-9113 ; . - Lecture Notes of the Unione Matematica Italiana, 12 .
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.
9783642213991
10.1007/978-3-642-21399-1 doi
Mathematics.
Functions of complex variables.
Differential equations, partial.
Potential theory (Mathematics).
Mathematics.
Potential Theory.
Functions of a Complex Variable.
Partial Differential Equations.
QA404.7-405
515.96
Harmonic Functions and Potentials on Finite or Infinite Networks [electronic resource] / by Victor Anandam. - X, 141p. online resource. - Lecture Notes of the Unione Matematica Italiana, 12 1862-9113 ; . - Lecture Notes of the Unione Matematica Italiana, 12 .
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.
9783642213991
10.1007/978-3-642-21399-1 doi
Mathematics.
Functions of complex variables.
Differential equations, partial.
Potential theory (Mathematics).
Mathematics.
Potential Theory.
Functions of a Complex Variable.
Partial Differential Equations.
QA404.7-405
515.96