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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
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