The Spectral Analysis of a Nuclear Resolvent Operator Associated with a Second Order Dissipative Differential Operator

Ugurlu E., BAYRAM E.

COMPUTATIONAL METHODS AND FUNCTION THEORY, cilt.17, sa.2, ss.237-253, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s40315-016-0185-8
  • Dergi Adı: COMPUTATIONAL METHODS AND FUNCTION THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.237-253
  • Anahtar Kelimeler: Dissipative operator, Trace class operator, Nuclear operator, Hilbert-Schmidt operator, Completeness theorem
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a new approach for the spectral analysis of a linear second order dissipative differential operator with distributional potentials. This approach is related with the inverse operator. We show that the inverse operator is a non-selfadjoint trace class operator. Using Lidskii's theorem, we introduce a complete spectral analysis of the second order dissipative differential operator. Moreover, we give a trace formula for the trace class integral operator.