Potential theory

Potential theory may be defined as the study of harmonic functions.

Spaces of harmonic functions

Since the Laplace equation is linear, the set of harmonic functions defined on a given domain is, in fact, a vector space. By defining suitable norms and/or inner products, one can exhibit sets of harmonic functions which form Hilbert or Banach spaces. In this fashion, one obtains such spaces as the Hardy space, Bloch space, and Bergmann space.

Related Topics:
Vector space - Norm - Inner product - Hilbert - Banach space - Hardy space - Bloch space - Bergmann space

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