Normal extensions for degenerate conformable fractional α -order differential operator

SERTBAŞ M.

Journal of Pseudo-Differential Operators and Applications, vol.14, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s11868-023-00507-9
  • Journal Name: Journal of Pseudo-Differential Operators and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Degenerate conformable differential operator, Minimal and maximal operators, Normal operator, Extension, Spectrum, EQUATIONS
  • Karadeniz Technical University Affiliated: Yes

Abstract

We establish all normal extensions domains structure on the weighed Hilbert space Lα2(H,(0,1)) for a formally normal minimal operators class defined by a degenerate conformable α-order differential-operator (Bu)(α)(t)+Au(t),α,t∈(0,1),where a positive selfadjoint B: H→ H has a closed range, KerB is a nontrivial subspace and A: H→ H is a selfadjoint operator. In addition, it is given the analysis of the spectrum set for any normal extensions.