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Stochastic processes --- Mathematical potential theory --- 517.57 --- 519.217.5 --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Additive functionals. Probabilistic potential theory --- 519.217.5 Additive functionals. Probabilistic potential theory --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Theorie du potentiel --- Theorie probabiliste

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Mathematical potential theory --- Potential theory (Mathematics) --- 517.57 --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Potential theory (Mathematics). --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Theorie du potentiel

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Complex analysis --- Analytical spaces --- 517.982 --- Hardy spaces --- #TCPW W8.0 --- 517.57 --- Spaces, Hardy --- Functional analysis --- Functions of complex variables --- Linear spaces with topology and order or other structures --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Hardy spaces. --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- 517.982 Linear spaces with topology and order or other structures

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These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.

Uniform algebras. --- Measure theory. --- Jensen measures. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Algebras, Uniform --- Banach algebras --- Commutative algebra --- Function algebras --- Jensen measures --- Measure theory --- Uniform algebras --- 517.57 --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Algèbres uniformes --- Mesure, Théorie de la --- Analytical spaces --- Harmonic analysis. Fourier analysis

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Conformal mapping --- Harmonic functions --- Potential theory (Mathematics) --- 517.57 --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Geometric function theory --- Mappings (Mathematics) --- Surfaces, Representation of --- Transformations (Mathematics) --- Mathematical potential theory