Nonlinear trigonometric approximations of multivariate function classes
Order-sharp estimates are established for the best N -term approximations of functions from Nikol’skii–Besov type classes B pq sm (T k ) with respect to the multiple trigonometric system T ( k ) in the metric of L r (T k ) for a number of relations between the parameters s , p , q , r , and m ( s =...
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| Published in: | Proceedings of the Steklov Institute of Mathematics Vol. 293; no. 1; pp. 2 - 36 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Moscow
Pleiades Publishing
01.05.2016
|
| Subjects: | |
| ISSN: | 0081-5438, 1531-8605 |
| Online Access: | Get full text |
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| Summary: | Order-sharp estimates are established for the best
N
-term approximations of functions from Nikol’skii–Besov type classes B
pq
sm
(T
k
) with respect to the multiple trigonometric system T
(
k
)
in the metric of
L
r
(T
k
) for a number of relations between the parameters
s
,
p
,
q
,
r
, and
m
(
s
= (
s
1
,...,
s
n
) ∈ R
+
n
, 1 ≤
p
,
q
,
r
≤ ∞,
m
= (
m
1
,...,
m
n
) ∈ N
n
,
k
=
m
1
+... +
m
n
). Constructive methods of nonlinear trigonometric approximation—variants of the so-called greedy algorithms—are used in the proofs of upper estimates. |
|---|---|
| ISSN: | 0081-5438 1531-8605 |
| DOI: | 10.1134/S0081543816040027 |