663 citations
- Centre National de la Recherche ScientifiqueFR14 papers
- Goddard Space Flight CenterUS14 papers
- Johns Hopkins University Applied Physics LaboratoryUS14 papers
- The University of Texas at San AntonioUS12 papers
- Sorbonne UniversitéFR11 papers
- University of Alaska AnchorageUS10 papers
- University of New HampshireUS10 papers
- University of SouthamptonGB10 papers
- Instituto de Astrofísica de CanariasES9 papers
- Universidad de La LagunaES9 papers
- University of California, Los AngelesUS9 papers
- Centro de AstrobiologíaES8 papers
8 papers · 1 filter
The boundary control approach to the Titchmarsh-Weyl function
S. A. Avdonin, V. S. Mikhaylov, A. V. Rybkin
We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the amplitude due to Simon and yields a new efficient method to ev…
The boundary control approach to inverse spectral theory
S. A. Avdonin, V. S. Mikhaylov
We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed…
On the inverse problem of the two-velocity tree-like graph
S. A. Avdonin, A. Choque Rivero, G. Leugering +1
In this article the authors continue the discussion in \cite{ALM} about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measuremen…
On an inverse problem for tree-like networks of elastic strings
S. A. Avdonin, G. Leugering, V. S. Mikhaylov
We consider the in-plane motion of elastic strings on tree-like network, observed from the 'leaves'. We investigate the inverse problem of recovering not only the physical properti…
Spectral Estimation Problem in Infinite Dimensional Spaces
S. A. Avdonin, V. S. Mikhaylov
We consider the generalized spectral estimation problem in infinite dimensional spaces. We solve this problem using the boundary control approach to inverse theory and provide an a…
On inverse dynamical and spectral problems for the wave and Schrödinger equations on finite trees. The leaf peeling method
S. A. Avdonin, V. S. Mikhaylov, K. B. Nurtazina
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguide…