On basicity of the system of eigenfunctions of one discontinuous spectral problem for second order differential equation for grand-Lebesgue space
TURKISH JOURNAL OF MATHEMATICS, cilt.44, ss.1595-1611, 2020 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 44
- Basım Tarihi: 2020
- Doi Numarası: 10.3906/mat-2003-20
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1595-1611
- Anahtar Kelimeler: Grand Lebesgue space, eigenfunctions, basicity, completeness, minimality, discontinuous spectral problem, PIECEWISE-LINEAR PHASE, MORREY, EXPONENTS
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
Basicity of the system of eigenfunctions of some discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space L-p) (-1; 1) is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace G(p)) (-1;1) of L-p) (-1; 1) generated by shift operator is considered. Basicity of the system of eigenfunctions for the space G(p) )(-1;1)circle plus C, 1 < p < +infinity, is proved. It is shown that the system of eigenfunctions of considered problem forms a basis for G(p)()) (-1;1), 1 < p < +infinity, after removal of any of its even-numbered functions.