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Harmonic analysis. Fourier analysis --- Probability theory

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Optics. Quantum optics --- Harmonic analysis. Fourier analysis --- optica --- Mathematical physics --- Probability theory --- Optics --- Fourier transformations --- System Analysis --- 535 --- Linear systems --- System analysis --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Physics --- Light --- Systems, Linear --- Differential equations, Linear --- Transformations, Fourier --- Transforms, Fourier --- Fourier analysis --- Transformations (Mathematics) --- Fourier transformations. --- Linear systems. --- Optics. --- System analysis. --- 535 Optics --- Network analysis --- Network science --- Physique

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517.44 --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- 517.44 Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Functional analysis --- Harmonic analysis. Fourier analysis --- Mathematical distribution theory

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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