K. Makarov

activity

19972004

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

30 citations · 37 across the 5 of their papers we have counts for

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13 papers · 1 filter

math.SP2004

The singularly continuous spectrum and non-closed invariant subspaces

Vadim Kostrykin, Konstantin A. Makarov

Let $A$ be a bounded self-adjoint operator on a separable Hilbert space $H$ and $H_{0} \subset H$ a closed invariant subspace of $A$ .…

math.SP2003★ 7 cited

(Modified) Fredholm Determinants for Operators with Matrix-Valued Semi-Separable Integral Kernels Revisited

Fritz Gesztesy, Konstantin A. Makarov

We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Gr…

math.SP2003

A generalization of the $t an 2Θ$ Theorem

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

Let $A$ be a bounded self-adjoint operator on a separable Hilbert space $H$ and $H_{0} \subset H$ a closed invariant subspace of $A$ .…

math.SP2002★ 30 cited

On the existence of solutions to the operator Riccati equation and the tanΘtheorem

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d>0 be the distance between the spectra of A and C. We prove that under…

math.SP2002

Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach

Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov

We introduce a new concept of unbounded solutions to the operator Riccati equation $A_{1} X - X A_{0} - X V X + V^{*} = 0$ and give a complete description of its solutions associated…

math.SP2002

$S L_{2} (R)$ , Exponential Herglotz Representations, and Spectral Averaging

Fritz Gesztesy, Konstantin A. Makarov

We revisit the concept of spectral averaging and point out its origin in connection with one-parameter subgroups of $S L_{2} (R)$ and the corresponding Möbius transformations. In pa…

The singularly continuous spectrum and non-closed invariant subspaces

(Modified) Fredholm Determinants for Operators with Matrix-Valued Semi-Separable Integral Kernels Revisited

A generalization of the tan2Θ Theorem

On the existence of solutions to the operator Riccati equation and the tanΘtheorem

Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach

SL2​(R), Exponential Herglotz Representations, and Spectral Averaging

A generalization of the $t an 2Θ$ Theorem

$S L_{2} (R)$ , Exponential Herglotz Representations, and Spectral Averaging