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Book Cover
Author Arsove, Maynard, 1922-

Title Algebraic potential theory / Maynard Arsove and Heinz Leutwiler
Published Providence, R.I. : American Mathematical Society, 1980
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Description 1 online resource (v, 130 pages) : illustrations
Series Memoirs of the American Mathematical Society, 1947-6221 ; v. 226
Memoirs of the American Mathematical Society ; no. 226. 0065-9266
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
Summary 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 unsymmetrical "mixed" lower and upper envelopes, formed relative to specific order on the first element and initial order on the second. The treatment makes essential use of a calculus of mixed envelopes, in which the main formulas and inequalities are derived through the use of certain semigroups of nonlinear operators. Techniques based on these operator semigroups are new even in the classical setting
Bibliography Includes bibliographical references (pages 128-130)
Notes Print version record
Subject Potential theory (Mathematics)
Riesz spaces.
Potential theory (Mathematics)
Riesz spaces.
Form Electronic book
Author Leutwiler, Heinz, 1939- author.
ISBN 1470406306