نتایج جستجو برای: riesz basis

تعداد نتایج: 385242  

1998
Sven Ehrich

It is well known that a shift invariant space S(N) generated by a compactly supported function N whose integer translates are a Riesz basis of S(N) has a unique orthonormal basis generated by a fundamental function of exponential decay. This result is extended by showing how the localisation carries over to the error of the orthogonal approximation P f] from S(N), i.e. localised error bounds ar...

2005
JEAN-MICHEL CORON E. Trélat

This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steadystate to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an expansion of the solution in a one-parameter Riesz basis of gene...

2009
Bernhard Haak Birgit Jacob Jonathan R. Partington Sandra Pott

This paper studies Volterra evolution equations from the point of view of control theory, in the case that the generator of the underlying semigroup has a Riesz basis of eigenvectors. Conditions for admissibility of the system’s control operator are given in terms of the Carleson embedding properties of certain discrete measures. Moreover, exact and null controllability are expressed in terms o...

2015
Sen Zhu Jiayin Zhao

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Severa...

Journal: :Journal of Machine Learning Research 2007
Yuesheng Xu Haizhang Zhang

Motivated by mathematical learning from training data, we introduce the notion of refinable kernels. Various characterizations of refinable kernels are presented. The concept of refinable kernels leads to the introduction of wavelet-like reproducing kernels. We also investigate a refinable kernel that forms a Riesz basis. In particular, we characterize refinable translation invariant kernels, a...

2007
Andreas Schneider

In this article, a new biorthogonal multiwavelet basis on the interval with complementary homogeneous Dirichlet boundary conditions of second order is presented. This construction is based on the multiresolution analysis onR introduced in [DHJK00] which consists of cubic Hermite splines on the primal side. Numerical results are given for the Riesz constants and both a non-adaptive and an adapti...

Journal: :Systems & Control Letters 2004
Bao-Zhu Guo Genqi Xu

This paper considers the controllability and Riesz basis generation property of linear infinite dimensional systems with group generators and one-dimensional admissible input operators. The corresponding results of [Advances in Mathematical Systems Theory, 2000, pp. 221-242] under the assumption of algebraic simplicity for eigenvalues of the generator are generalized to the case in which the ei...

Journal: :Applied Mathematics and Computer Science 2013
Sergei Avdonin Abdon E. Choque Rivero Luz de Teresa

We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent resu...

2007
Sven Ehrich

It is well known that a shift invariant space S(N) generated by a compactly supported function N whose integer translates are a Riesz basis of S(N) has a unique orthonormal basis generated by a fundamental function of exponential decay. This result is extended by showing how the localisation carries over to the error of the orthogonal approximation P f] from S(N), i.e. localised error bounds ar...

Journal: :J. Computational Applied Mathematics 2018
Nabi Chegini Rob P. Stevenson

A Laplace type boundary value problem is considered with a generally discontinuous diffusion coefficient. A domain decomposition technique is used to construct a piecewise tensor product wavelet basis that, when normalised w.r.t. the energy-norm, has Riesz constants that are bounded uniformly in the jumps. An adaptive wavelet Galerkin method is applied to solve the boundary value problem with t...

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