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On Vladimir Markov type inequality in Lp norms on the interval [-1; 1]

Baran Mirosław, Ozorka Paweł

Science, Technology and Innovation

2019

Vol. 7, no. 4

9--12

We prove inequality ||P(k)||Lp(-1;1)≤Bp||Tn(k)||Lp(-1;1)n^(2/p) ||P||Lp(-1;1); where Bp are constants independent of n = deg P with 1 ≤ p ≤ 2, which is sharp in the case k ≥ 3. A method presented in this note is based on a factorization of linear operator of k-th derivative throughout normed spaces of polynomial equipped with a Wiener type norm.

On Projection Based Operators in lp Space for Exact Similarity Search

Wichert A., Moreira C.

Fundamenta Informaticae

2015

Vol. 136, nr 4

461--474

We investigate exact indexing for high dimensional lp norms based on the 1-Lipschitz property and projection operators. The orthogonal projection that satisfies the 1-Lipschitz property for the lp norm is described. The adaptive projection defined by the first principal component is introduced.

An application of the Lp-norm in robust weighted averaging of biomedical signals

Pander T., Przybyła T., Czabański R.

Journal of Medical Informatics & Technologies

2013

Vol. 22

71--78

Averaging is one of the basic methods of statistical analysis of experimental data where the response of the system is periodic or quasi-periodic. As long as the noise are Gaussian, the standard averaging leads to good results and effective noise reduction. However, when the distortions have impulsive nature, then such an approach leads to a deterioration of the system. In this case the robust methods should be applied which are characterized by resistance to a statistical sample spoken. In this work a robust averaging method based on the minimization of a scalar criterion function using a Lp-norm functions are presented. The effectiveness of the proposed method was tested in an averaging periods aligned ECG signal cycles in the presence of impulse noise.