Sampling discretization of integral norms of the hyperbolic cross polynomials

05/12/2020
by   Vladimir Temlyakov, et al.
0

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses. It is shown that recently developed techniques allow us to improve the known results in this direction.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/25/2020

Sampling discretization of integral norms

The paper is devoted to discretization of integral norms of functions fr...
research
01/02/2022

On universal sampling representation

For the multivariate trigonometric polynomials we study convolution with...
research
08/20/2022

Some improved bounds in sampling discretization of integral norms

The paper addresses a problem of sampling discretization of integral nor...
research
05/04/2023

A Hyperbolic Extension of Kadison-Singer Type Results

In 2013, Marcus, Spielman, and Srivastava resolved the famous Kadison-Si...
research
04/02/2021

A remark on discretization of the uniform norm

Discretization of the uniform norm of functions from a given finite dime...
research
09/18/2021

Sampling discretization of integral norms and its application

The paper addresses the problem of sampling discretization of integral n...
research
04/28/2021

On exact discretization of the L_2-norm with a negative weight

For a subspace X of functions from L_2 we consider the minimal number m ...

Please sign up or login with your details

Forgot password? Click here to reset