K. Makarov

activity

19972008

most citedOn the existence of solutions to the operator Riccati equation and the tanΘtheorem

30 citations · 40 across the 7 of their papers we have counts for

collaborators

Showing 1999 · math.SPShow all

4 papers · 2 filters

math.SP1999

Monotonicity and Concavity Properties of The Spectral Shift Function

F. Gesztesy, K. A. Makarov, A. K. Motovilov

Let $H_{0}$ and $V (s)$ be self-adjoint, $V, V^{'}$ continuously differentiable in trace norm with $V^{''} (s) \geq 0$ for $s \in (s_{1}, s_{2})$ , and denote by ${E_{H (s)} (λ)}_{λ \in R}$ the fami…

math.SP1999

The Xi Operator and its Relation to Krein's Spectral Shift Function

Fritz Gesztesy, Konstantin A. Makarov

We explore connections between Krein's spectral shift function $ξ (λ, H_{0}, H)$ associated with the pair of self-adjoint operators $(H_{0}, H)$ , $H = H_{0} + V$ in a Hilbert space $\calH$ and t…

math.SP1999

Some Applications of the Spectral Shift Operator

Fritz Gesztesy, Konstantin A. Makarov

The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operator…

math.SP1999

The Spectral Shift Operator

Fritz Gesztesy, Konstantin A. Makarov, Serguei N. Naboko

We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-val…