10 citations · 59 across the 16 of their papers we have counts for
4 papers · 1 filter
Construction of a Sturm-Liouville vessel using Gelfand-Levitan theory. On solution of the Korteweg-de Vries equation in the first quadrant
Andrey Melnikov
Using Gelfand-Levitan theory on a half line, we construct a vessel for the class of potentials, whose spectral functions satisfy a certain regularity assumption. When the singular…
On the class SI of J-contractive functions intertwining solutions of linear differential equations
D. Alpay, A. Melnikov, V. Vinnikov
In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transf…
Overdetermined conservative 2D Systems, Invariant in One Direction and a Generalization of Potapov's theorem
Andrey Melnikov, Victor Vinnikov
This work is a direct continuation of the authors work arXiv:0812.3779v1. A special case of conservative overdetermined time invariant 2D systems is developed and studied. Defining…
Overdetermined 2D Systems Invariant in One Direction and Their Transfer Functions
Andrey Melnikov, Victor Vinnikov
In this work we develop a theory of Vessels. This object arises in the study of overdetermined 2D systems invariant in one of the variables, which are usually called time invariant…