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Journal Article
Universal Sampling Discretization
2023
Overview
Let
X
N
be an
N
-dimensional subspace of
L
2
functions on a probability space
(
Ω
,
μ
)
spanned by a uniformly bounded Riesz basis
Φ
N
. Given an integer
1
≤
v
≤
N
and an exponent
1
≤
p
≤
2
, we obtain universal discretization for the integral norms
L
p
(
Ω
,
μ
)
of functions from the collection of all subspaces of
X
N
spanned by
v
elements of
Φ
N
with the number
m
of required points satisfying
m
≪
v
(
log
N
)
2
(
log
v
)
2
. This last bound on
m
is much better than previously known bounds which are quadratic in
v
. Our proof uses a conditional theorem on universal sampling discretization, and an inequality of entropy numbers in terms of greedy approximation with respect to dictionaries.
Publisher
Springer US,Springer Nature B.V
Subject
