Spectral Theory Network  

Loughborough Y. Kurylev's research is related to the Gelfand inverse boundary spectral problem, i.e. the problem of the reconstruction of an elliptic operator (together with the underlying manifold with boundary) from the restriction on the boundary of the Schwartz kernel of the resolvent. His main achievements include the analysis of this problem on Riemann manifolds and also the inverse problem for nonselfadjoint operators. In addition he has worked on the inverse problem for Maxwell's equations A. Pushnitski's research belongs to the area of trace class perturbation theory of selfadjoint operators in a Hilbert space. More precisely, the main object of his study is Krein's spectral shift function (SSF). In 1998, he found a formula representation for the SSF for the case of perturbations of a definite sign. In 19992000 he applied this representation to obtain a number of results for the SSF of the Schrödinger operator, including pointwise and integral estimates and semiclassical asymptotics. 

