Spectral expansion for the singular Dirac system with impulsive conditions

Pasaoglu Allahverdiev B., TUNA H.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.5, pp.2527-2545, 2018 (SCI-Expanded, Scopus, TRDizin)

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1803-79
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2527-2545
  • Keywords: Dirac operator, impulsive conditions, singular point, spectral function, Parseval equality, spectral expansion, STURM-LIOUVILLE PROBLEMS, EIGENVALUE PROBLEM, OPERATORS, SCHRODINGER, SCATTERING
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.