On Banach frameness of degenerate weighted exponential system
This work deals with the frameness of weighted exponential system E ( ω , Z ) = { ω ( t ) e i n t } n ∈ Z in the space L p ( − π , π ) , p > 1 , with the weight function ω ( t ) of general form. Basis properties of E ( ω , Z ) in L p ( − π , π ) , p > 1 , are studied, in other words, the crite...
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| Veröffentlicht in: | Fixed point theory and algorithms for sciences and engineering Jg. 2025; H. 1; S. 26 - 15 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham
Springer International Publishing
23.09.2025
Springer Nature B.V SpringerOpen |
| Schlagworte: | |
| ISSN: | 2730-5422, 2730-5422 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This work deals with the frameness of weighted exponential system
E
(
ω
,
Z
)
=
{
ω
(
t
)
e
i
n
t
}
n
∈
Z
in the space
L
p
(
−
π
,
π
)
,
p
>
1
, with the weight function
ω
(
t
)
of general form. Basis properties of
E
(
ω
,
Z
)
in
L
p
(
−
π
,
π
)
,
p
>
1
, are studied, in other words, the criteria of completeness, minimality and basicity of the system
E
(
ω
,
Z
)
in the space
L
p
(
−
π
,
π
)
,
p
>
1
, are given. Sufficient conditions for the completeness and minimality of
E
(
ω
,
Z
∖
F
)
in
L
p
(
−
π
,
π
)
,
p
>
1
, are found, where
F
is an arbitrary finite nonempty subset of the set of integers
Z
. A different method to prove that the system
E
(
ω
,
Z
∖
F
)
does not form a Schauder basis for
L
p
(
−
π
,
π
)
,
p
>
1
, is given. Theorem on a property of expansion system and criterion of Banach frameness for
E
(
ω
,
Z
)
in
L
p
(
−
π
,
π
)
,
p
>
1
, are proved. In particular, it is proved that the system
E
(
ω
,
Z
)
with defect cannot form atomic decomposition for
L
p
(
−
π
,
π
)
,
p
>
1
. The obtained results are the generalizations of those on the atomic decomposition of power weighted exponential system in
L
p
(
−
π
,
π
)
,
p
>
1
, and the frameness of weighted exponential system in
L
2
(
−
π
,
π
)
. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 2730-5422 2730-5422 |
| DOI: | 10.1186/s13663-025-00805-5 |