Higher order spectral shift, II. Unbounded case

Details Higher order spectral shift, II. Unbounded case Higher order spectral shift, II. Unbounded case

2009-01-16

arxiv.org/abs/0901.2393v2

Mathematics

Spectral Theory

13 pages; typos corrected; to appear in Indiana Univ. Math. J

Scientific paper

We construct higher order spectral shift functions, which represent the remainders of Taylor-type approximations for the value of a function at a perturbed self-adjoint operator by derivatives of the function at an initial unbounded operator. In the particular cases of the zero and the first order approximations, the corresponding spectral shift functions have been constructed by M. G. Krein and L. S. Koplienko, respectively. The higher order spectral shift functions obtained in this paper can be expressed recursively via the lower order ones, in particular, Krein's and Koplienko's spectral shift functions. This extends the recent results of Dykema and Skripka for bounded operators.

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