30 citations · 37 across the 5 of their papers we have counts for
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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…
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 and give a complete description of its solutions associated…
, 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 and the corresponding Möbius transformations. In pa…
On a Subspace Perturbation Problem
Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov
We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let and be bounded self-adjoint operators. Assu…
Matrix-Valued Generalizations of the Theorems of Borg and Hochstadt
E. D. Belokolos, F. Gesztesy, K. A. Makarov +1
We prove a generalization of the well-known theorems by Borg and Hochstadt for periodic self-adjoint Schrödinger operators without a spectral gap, respectively, one gap in their sp…