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Algebraic potential theory

About this Title

Maynard Arsove and Heinz Leutwiler

Publication: Memoirs of the American Mathematical Society
Publication Year: 1980; Volume 23, Number 226
ISBNs: 978-0-8218-2226-5 (print); 978-1-4704-0630-1 (online)
DOI: https://doi.org/10.1090/memo/0226
MathSciNet review: 550855
MSC: Primary 31-02; Secondary 06F05, 31D05, 46A40

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Table of Contents

Chapters

  • Introduction
  • 1. Mixed lattice semigroups
  • 2. Equivalent forms of Axiom I
  • 3. The calculus of mixed envelopes
  • 4. Strong suprema and infima
  • 5. Harmonic ideals and bands
  • 6. Preharmonic and potential bands
  • 7. Riesz decompositions and projections
  • 8. Quasibounded and singular elements
  • 9. Superharmonic semigroups
  • 10. Pseudo projections and balayage operators
  • 11. Quasi-units and generators
  • 12. Infinite series of quasi-units
  • 13. Generators
  • 14. Increasing additive operators
  • 15. Potential operators and induced specific projection bands
  • 16. Some remarks on duals and biduals
  • 17. Axioms for the hvperharmonic case
  • 18. The operators $S$ and $Q$
  • 19. The weak band of cancellable elements
  • 20. Hyperharmonic semigroups
  • 21. The classical superharmonic semigroups and some abstractions