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 Bergman space.
Read more about this topic: Potential Theory
Famous quotes containing the words spaces of, spaces, harmonic and/or functions:
“through the spaces of the dark
Midnight shakes the memory
As a madman shakes a dead geranium.”
—T.S. (Thomas Stearns)
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—Ralph Waldo Emerson (1803–1882)
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—Kyle D. Pruett (20th century)
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—Cyril Connolly (1903–1974)