نتایج جستجو برای: riesz bases

تعداد نتایج: 69716  

Journal: :Math. Comput. 2011
Rong-Qing Jia Wei Zhao

We investigate Riesz bases of wavelets in Sobolev spaces and their applications to numerical solutions of the biharmonic equation and general elliptic equations of fourth-order. First, we study bicubic splines on the unit square with homogeneous boundary conditions. The approximation properties of these cubic splines are established and applied to convergence analysis of the finite element meth...

2000
Werner Kozek Götz Pfander Jörn Ungermann Georg Zimmermann

In this paper we compare different transmultiplexer structures with respect to the ISI/ICI occuring for typical time–invariant channels. In particular we consider wavelet–type, Gabor-type (the class containing OFDM and DMT) and Wilson-type (offset-QAM/OFDM) transmultiplexer. We present both theoretical results (based on a recently developed perturbation theory of coherent Riesz bases) and numer...

Journal: :IJWMIP 2013
Yun-Zhang Li Yan Zhang

This talk addresses vector-valued subspace Gabor frames with rational time-frequency product. By introduction of a suitable Zak transform matrix, we characterize vector-valued subspace Gabor frames, Riesz bases and orthonorrmal bases, and the uniqueness of Gabor duals of type I and type II. Using the uniqueness results, we extend the classical Balian-Low theorem to vector-valued subspace Gabor ...

2001
Radu V. Balan

In this paper we present topology aspects in non-localization results. A well-known such no-go result is the BalianLow theorem that states the generator of a Weyl-Heisenberg Riesz basis cannot be well time-frequency localized. More general, the statement applies to multi WH Riesz bases, or super frames as well. These results turn out to be connected to non-triviality of a complex vector bundle....

2008
Hans Zwart

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (co...

2005
Jan Maes Adhemar Bultheel

In this paper we use the lifting scheme to construct biorthogonal spline wavelet bases on regularly refined non-uniform grids. The wavelets have at least one vanishing moment and on each resolution level they form an L2 Riesz basis. Furthermore we are interested in determining the exact range of Sobolev exponents for which the complete multilevel system forms a Riesz basis. Hereto we need to ex...

Journal: :Bulletin of the American Mathematical Society 2001

Journal: :International Journal of Mathematics and Mathematical Sciences 2003

Journal: :Communications of the Korean Mathematical Society 2004

Journal: :Applied and Computational Harmonic Analysis 1995

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