Normal Extensions of a First Order Differential Operator

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FILOMAT, vol.28, no.5, pp.917-923, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.2298/fil1405917i
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.917-923
  • Karadeniz Technical University Affiliated: Yes


In the paper of W.N. Everitt and A. Zettl [26] in scalar case, all selfadjoint extensions of the minimal operator generated by Lagrange-symmetric any order quasi-differential expression with equal deficiency indexes in terms of boundary conditions are described by Glazman-Krein-Naimark method for regular and singular cases in the direct sum of corresponding Hilbert spaces of functions. In this work, by using the method of Calkin-Gorbachuk theory all normal extensions of the minimal operator generated by fixed order linear singular multipoint differential expression l = (l(-), l(1), ... , l(n), l(+)), l(-/+) = d/dt + A(-/+), l(k) = d/dt + A(k) where the coefficients A(-/+), A(k) are selfadjoint operator in separable Hilbert spaces H--/+, H-k, k = 1, ... , n, n is an element of N respectively, are researched in the direct sum of Hilbert spaces of vector-functions