New aspects of Beurling–Lax shift invariant subspaces

Tan, Lei; Qian, Tao; Chen, Qiuhui

doi:10.1016/j.amc.2014.12.147

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Cited by 2 publications

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“…For fast expanding a given function into a TM system the adaptive Fourier decomposition (AFD) was proposed that is related to the Beurling-Lax decomposition of the Hardy space into the direct sum of the forward-and the backward-shift invariant subspaces ( [9,21]). AFD theory and algorithm have been generalized to matrix-valued functions defined in the disc ( [1]) and in the ball of several complex variables ( [2]).…”

Section: Introductionmentioning

confidence: 99%

A sufficient condition for n-Best Kernel Approximation in Reproducing Kernel Hilbert Spaces

Qu¹,

Qian²,

Deng³

2020

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We show that if a reproducing kernel Hilbert space H K , consisting of functions defined on E, enjoys Double Boundary Vanishing Condition (DBVC) and Linear Independent Condition (LIC), then for any preset natural number n, and any function f ∈ H K , there exists a set of n parameterized multiple kernels Kw1 ,By applying the theorem of this paper we show that the Hardy space and the Bergman space, as well as all the weighted Bergman spaces in the unit disc all possess n-best approximations. In the Hardy space case this gives a new proof of a classical result. Based on the obtained results we further prove existence of n-best spherical Poisson kernel approximation to functions of finite energy on the real-spheres.

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