Algebraic potential theory /

Global aspects of classical and axiomatic potential theory are developed in a purely algebraic way, in terms of a new algebraic structure called a mixed lattice semigroup. This generalizes the notion of a Riesz space (vector lattice) by replacing the usual symmetrical lower and upper envelopes by un...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Arsove, Maynard, 1922-, Leutwiler, Heinz, 1939- (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, R.I. : American Mathematical Society, 1980.
Series:Memoirs of the American Mathematical Society ; no. 226.
Subjects:
Riesz spaces.
Potential theory (Mathematics)
Espaces de Riesz.
Théorie du potentiel.
Riesz spaces
Online Access:Texto completo
Table of Contents:
  • Introduction
  • Mixed lattice semigroups
  • Equivalent forms of Axiom I
  • The calculus of mixed envelopes
  • Strong suprema and infima
  • Harmonic ideals and bands
  • Preharmonic and potential bands
  • Riesz decompositions and projections
  • Quasibounded and singular elements
  • Superharmonic semigroups
  • Pseudo projections and balayage operators
  • Quasi-units and generators
  • Infinite series of quasi-units
  • Generators
  • Increasing additive operators
  • Potential operators and induced specific projection bands
  • Some remarks on duals and biduals
  • Axioms for the hvperharmonic case
  • The operators S and Q
  • The weak band of cancellable elements
  • Hyperharmonic semigroups
  • The classical superharmonic semigroups and some abstractions.

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