Orlicz spaces, spline systems, and Brownian motion

DOI10.1007/BF01198003zbMath0814.46022MaRDI QIDQ1801486

Zbigniew Ciesielski

Publication date: 12 June 1995

Published in: Constructive Approximation (Search for Journal in Brave)

zbMATH Keywords

Brownian motionWiener measureFranklin systemOrlicz spacescovarianceHölder classescomposition of two Borel functionscorrelation of two random variablesorthogonal spline expansions of the Franklin typetwo-dimensional Gaussian vector

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Brownian motion (60J65) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Spline approximation (41A15) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Analysis of variance and covariance (ANOVA) (62J10)

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Cites Work

• Best constants in moment inequalities for linear combinations of independent and exchangeable random variables
• Constructive function theory and spline systems
• Properties of the orthonormal Franklin system, II
• Estimates for spline orthonormal functions and for their derivatives
• Construction of an orthonormal basis in $C^{m}(I^{d})$ and $W^{m}_{p}(I^{d})$
• Properties of the orthonormal Franklin system
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