Semigroup-theoretic proofs of the central limit theorem and other theorems of analysis

DOI10.1007/BF02195925zbMath0326.47043MaRDI QIDQ1225828

Jerome A. Goldstein

Publication date: 1976

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/134172

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Groups and semigroups of linear operators (47D03) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (13)

Emergence of Freidlin-Wentzell's transmission conditions as a result of a singular perturbation of a semigroup ⋮ Differential equations in a Banach space ⋮ On the product formulas for \(C\)-semigroups ⋮ Almost-periodic solutions of second-order differential equations ⋮ The Feynman-Kac formula and the Hamilton-Jacobi equation ⋮ A tribute to Jerome (Jerry) Arthur Goldstein ⋮ Approximation of unbounded functions and applications to representations of semigroups ⋮ Some developments in semigroups of operators since Hille-Phillips ⋮ A semigroup-theoretic proof of the law of large numbers ⋮ Lax-type theorems and a unified approach to some limit theorems in probability theory with rates ⋮ A semigroup-theoretic proof of Poisson's limit law ⋮ Product formulas for semigroups with elliptic generators ⋮ Product formulas for solutions of initial value partial differential equations. I

Cites Work

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• Note on product formulas for operator semigroups
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• On the Product of Semi-Groups of Operators
• The Feynman Integral
• Product formulas, nonlinear semigroups, and addition of unbounded operators
• Convergence of Sequences of Semigroups of Nonlinear Operators with an Application to Gas Kinetics
• Feynman Integrals and the Schrödinger Equation
• An elementary proof of the central limit theorem

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