Markus Passenbrunner (2014)
Studia Mathematica
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We prove that given any natural number k and any dense point sequence (tₙ), the corresponding orthonormal spline system is an unconditional basis in reflexive .
Černá, Dana, Finěk, Václav, Šimůnková, Martina
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In signal and image processing as well as in numerical solution of differential equations, wavelets with short support and with vanishing moments are important because they have good approximation properties and enable fast algorithms. A B-spline of order is a spline function that has minimal support among all compactly supported refinable functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed Riesz wavelet bases of with vanishing moments based...
Peter Oswald (2006)
Banach Center Publications
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We extend results on constructing semiorthogonal linear spline prewavelet systems in one and two dimensions to the case of irregular dyadic refinement. In the one-dimensional case, we obtain sharp two-sided inequalities for the -condition, 1 < p < ∞, of such systems.
Leszek Skrzypczak (1989)
Banach Center Publications
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Zygmunt Wronicz (2002)
Annales Polonici Mathematici
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Chebyshevian box splines were introduced in [5]. The purpose of this paper is to show some new properties of them in the case when the weight functions are of the form , where the functions are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.
Wiesław Szwiec
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The paper is devoted to a certain problem in the theory of synthesis of optimal control. The fundamental results of research in the synthesis of optimal control for second order systems are given in [1], [2], [5], [10]. In particular, in [2] and [5] some specific nonlinear systems are investigated, namely the systems related with the differential equations of the forms̈ + F(s,ṡ) = u or s̈ + F(s,ṡ,u) = 0where u is a control parameter in the interval [—1,1]. Some results concerning third...
Kazimierz Malanowski
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A family of parameter dependent optimal control problems with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value h₀ of the parameter, a solution of exists. It is shown that if (i) independence, controllability and coercivity conditions are satisfied at the reference solution, then (ii) for each h from a neighborhood of h₀, a locally unique solution to and the associated Lagrange...
Magnus Egerstedt, Clyde Martin (2003)
ESAIM: Control, Optimisation and Calculus of Variations
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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.
Rodrigues, R.C., Torres, D.F.M. (2006)
Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino
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Fausto Gozzi (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
Ferenc Weisz (2001)
Studia Mathematica
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We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space to if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if...
Fausto Gozzi (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
Magnus Egerstedt, Clyde Martin (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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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.