Analytic Embedding and Mean Square Approximation
نویسندگان
چکیده
منابع مشابه
Thomson’s Theorem on Mean Square Polynomial Approximation
In 1991, J. E. Thomson determined completely the structure of H2(μ), the closed subspace of L2(μ) that is spanned by the polynomials, whenever μ is a compactly supported measure in the complex plane. As a consequence he was able to show that if H2(μ) = L2(μ), then every function f ∈ H2(μ) admits an analytic extension to a fixed open set Ω, thereby confirming in this context a phenomenon noted e...
متن کاملBest Approximation in the Mean by Analytic and Harmonic Functions
For n ≥ 2, let Bn denote the unit ball in R, and for p ≥ 1 let L denote the Banach space of p-summable functions on Bn. Let L p h(Bn) denote the subspace of harmonic functions on Bn that are p-summable. When n = 2, we often write D instead of B2, and we let A denote the Bergman space of analytic functions in L. Let ω be a function in L. We are interested in finding the best approximation to ω i...
متن کاملMean square convergence analysis for kernel least mean square algorithm
In this paper, we study the mean square convergence of the kernel least mean square (KLMS). The fundamental energy conservation relation has been established in feature space. Starting from the energy conservation relation, we carry out the mean square convergence analysis and obtain several important theoretical results, including an upper bound on step size that guarantees the mean square con...
متن کاملMean Square Estimation
The problem of parameter estimation in linear model is pervasive in signal processing and communication applications. It is often common to restrict attention to linear estimators, which simplifies the implementation as well as the mathematical derivations. The simplest design scenario is when the second order statistics of the parameters to be estimated are known and it is desirable to minimiz...
متن کاملLeast Mean Square Algorithm
The Least Mean Square (LMS) algorithm, introduced by Widrow and Hoff in 1959 [12] is an adaptive algorithm, which uses a gradient-based method of steepest decent [10]. LMS algorithm uses the estimates of the gradient vector from the available data. LMS incorporates an iterative procedure that makes successive corrections to the weight vector in the direction of the negative of the gradient vect...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1967
ISSN: 0002-9939
DOI: 10.2307/2035122