Dissipative fractal Dirac equations

Allahverdiyev B., TUNA H.

Asian-European Journal of Mathematics, vol.19, no.4, 2026 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 4
  • Publication Date: 2026
  • Doi Number: 10.1142/s1793557125500871
  • Journal Name: Asian-European Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: completeness, Fractal Dirac equations, scattering matrix, selfadjoint dilation
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

This study investigates fractal Dirac problems in the regular case. The initial presentation of the subject matter is focused on dissipative expansions for this class of equations. The construction of a scattering matrix corresponding to the dilation is achieved by developing a selfadjoint dilation of the maximal dissipative operator, in conjunction with its incoming and outgoing spectral representations in each instance. Furthermore, a functional model of the maximal dissipative operator is developed, and its characteristic function is derived. The establishment of completeness theorems for these operators is shown to be of central significance.