Riesz basis property of system of root functions of second-order differential operator with involution
The properties of the root functions are studied for an arbitrary operator generated in L 2 (−1, 1) by the operation with involution of the form Lu = − u ″( x )+ αu ″(− x )+ q ( x ) u ( x )+ qν ( x ) u ( ν ( x )), where α ∈ (−1, 1), ν ( x ) is an absolutely continuous involution of the segment [−1,...
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| Veröffentlicht in: | Differential equations 2017, Vol.53 (1), p.33-46 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The properties of the root functions are studied for an arbitrary operator generated in
L
2
(−1, 1) by the operation with involution of the form
Lu
= −
u
″(
x
)+
αu
″(−
x
)+
q
(
x
)
u
(
x
)+
qν
(
x
)
u
(
ν
(
x
)), where
α
∈ (−1, 1),
ν
(
x
) is an absolutely continuous involution of the segment [−1, 1] and the coefficients
q
(
x
) and
qν
(
x
) are summable functions on (−1, 1). Necessary and sufficient conditions are obtained for the unconditional basis property in
L
2
(−1, 1) for the system of the root functions of the operator. |
|---|---|
| ISSN: | 0012-2661 1608-3083 |
| DOI: | 10.1134/S0012266117010049 |