Systems of dilated functions: Completeness, minimality, basisness
The completeness, minimality, and basis property in L 2 [0, π ] and L p [0, π ], p ≠ 2, are considered for systems of dilated functions u n ( x ) = S ( nx ), n ∈ N, where S is the trigonometric polynomial S ( x ) = Σ k =0 m a k sin( kx ), a 0 a m ≠ 0. A series of results are presented and several un...
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| Veröffentlicht in: | Functional analysis and its applications 2017-07, Vol.51 (3), p.236-239 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The completeness, minimality, and basis property in
L
2
[0,
π
] and
L
p
[0,
π
],
p
≠ 2, are considered for systems of dilated functions
u
n
(
x
) =
S
(
nx
),
n
∈ N, where
S
is the trigonometric polynomial
S
(
x
) = Σ
k
=0
m
a
k
sin(
kx
),
a
0
a
m
≠ 0. A series of results are presented and several unanswered questions are mentioned. |
|---|---|
| ISSN: | 0016-2663 1573-8485 |
| DOI: | 10.1007/s10688-017-0188-x |