Magnus Egerstedt, Clyde Martin (2010)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.
Demirici, Kamil, Dirik, Fadime (2011)
Applied Mathematics E-Notes [electronic only]
Cao, Jiading (1997)
International Journal of Mathematics and Mathematical Sciences
R. Averkamp, C. Houdré (2006)
ESAIM: Probability and Statistics
Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.
Eckart Schmidt (1970)
Mathematische Zeitschrift
Erich Novak (1988)
Numerische Mathematik
J.P., Thiry, S. Thiran (1987)
Numerische Mathematik
Menegatto, V. A., Peron, A. P. (2002)
International Journal of Mathematics and Mathematical Sciences
Lin, Shaobo, Cao, Feilong (2011)
Journal of Inequalities and Applications [electronic only]
Gilles Godefroy, V. Indumathi (2001)
Revista Matemática Complutense
In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.
Ferenc Weisz (2004)
Studia Mathematica
A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).
Grzegorz Lewicki (1993)
Commentationes Mathematicae Universitatis Carolinae
Let be a finite dimensional Banach space and let be a hyperplane. Let . In this note, we present sufficient and necessary conditions on being a strongly unique best approximation for given . Next we apply this characterization to the case of and to generalization of Theorem I.1.3 from [12] (see also [13]).
Kroó, András, Pinkus, Allan (2010)
Surveys in Approximation Theory (SAT)[electronic only]
M.R. Osborne, K. Jittorntrum (1980)
Numerische Mathematik
S. Dutta, Darapaneni Narayana (2007)
Colloquium Mathematicae
We characterize strongly proximinal subspaces of finite codimension in C(K) spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in C(K) is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of C(K).
Jasson Vindas (2008)
Publications de l'Institut Mathématique
A. Begumisa, Ian Robinson (1990/1991)
Numerische Mathematik
Bernd Stockenberg (1977)
Manuscripta mathematica
Zhidkov, Peter E. (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Carlos Benítez, Manuel Fernández, María L. Soriano (1996)
Extracta Mathematicae