The regularized trace of a self adjoint differential operator of higher order with unbounded operator coefficient

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Adiguzelov E., Sezer Y.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, pp.2113-2121, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218
  • Publication Date: 2011
  • Doi Number: 10.1016/j.amc.2011.07.028
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.2113-2121

Abstract

Let L0 and L be operators which are formed by the differential expressions in the space H1 = L2(0,p; >H), with same boundary conditions, where H is an infinite dimensional separable Hilbert space. Here, A is an unbounded self adjoint operator in H and, for every x 2 [0,p], Q(x) is a selfadjoint trace class operator in H. Assuming the operator A and the operator function Q(x) satisfy some additional conditions, we found trace formula for the operator of higher order with unbounded operator coefficient.