On basicity of the system of eigenfunctions of one discontinuous spectral problem for second order differential equation for grand-Lebesgue space

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Zeren Y., Ismailov M., Sirin F.

TURKISH JOURNAL OF MATHEMATICS, cilt.44, ss.1595-1611, 2020 (SCI-Expanded) identifier identifier

  • 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
  • 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.