31D05 Axiomatic potential theory

Overview

31D05 studies axiomatic potential theory in axiomatic potential theory. It studies potential theory from an axiomatic viewpoint, isolating the abstract properties that support harmonic and balayage constructions.

Related Wikipedia Page

Axiomatic Potential Theory (Wikipedia)

Useful Links

• Axiomatic Potential Theory (Wikipedia)
• Potential theory (Wikipedia)
• Harmonic measure (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for axiomatic potential theory
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to characterize general potential spaces without committing to a particular ambient geometry.

Applications

• Axiomatic harmonic spaces
• Balayage and sweeping
• Abstract boundary theory

References

• Doob, J.L. (1984) Classical Potential Theory and Its Probabilistic Counterpart. New York, NY: Springer.
• Brelot, M. (1960) Lectures on Potential Theory. Tata Institute.

Recommended Textbooks

• Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill.
• Topic-focused textbook search (n.d.) Axiomatic potential theory. Available via Amazon search.