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Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.


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TL;DR: In this article, a number of compact biorthogonal wavelets are constructed in which the global convergent homotopy method is used for different N and N. The relationship of N, N and solutions' quantity is discussed in detail.
Abstract: The biorthogonal wavelets families are usedwidely because they have compact support, complete symmetry and linear phase. According to Bezout’s theorem,the biorthogonal wavelets available now are only some particular examples of total solutions. The quantity of solutions is decided jointly by the scaling function vanishingmoment N and dual vanishing moment N. The relationship of N, N and solutions’ quantity is discussed in detail.According to the constraint conditions which the compactbiorthogonal wavelets satisfy, a number of biorthogonalwavelets are constructed in which the global convergenthomotopy method is used for different N and N. The filter coefficients and plots of scaling function, dual scalingfunction, wavelet function and dual wavelet function aregiven.

5 citations

Journal ArticleDOI
TL;DR: For the minimal splines of arbitrary order on a non-uniform grid, a system of linear functionals biorthogonal to the system of coordinate splines is constructed in this article.
Abstract: For the minimal splines of arbitrary order on a nonuniform grid, a system of linear functionals biorthogonal to the system of coordinate splines is constructed. The matrices of refining and sparsing decompositions are obtained for the spaces of splines of arbitrary order associated with infinite and finite nonuniform grids on an interval and on a segment, respectively.

5 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the statistical behavior of entanglement over the Bures-Hall ensembles as measured by the simplest form of an entropy -the quantum purity, and derived recurrence relations of the underlying integrals over the Cauchy-Laguerre polynomials.
Abstract: The Bures-Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures-Hall ensemble as measured by the simplest form of an entanglement entropy - the quantum purity. The main results of this work are the exact second and third moment expressions of quantum purity valid for any subsystem dimensions, where the corresponding results in the literature are limited to the scenario of equal subsystem dimensions. In obtaining the results, we have derived recurrence relations of the underlying integrals over the Cauchy-Laguerre biorthogonal polynomials that may be of independent interest.

5 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202329
2022105
202155
202058
201960