16 citations · 35 across the 8 of their papers we have counts for
11 papers
Stability of determinacy and inverse spectral problems for Jacobi operators
Rafael del Rio, Luis O. Silva
This work studies the interplay between Green functions, the index of determinacy of spectral measures and interior finite rank perturbations of Jacobi operators. The index of dete…
A direct proof of F. Riesz representation Theorem
Rafael del Rio, Asaf Franco, Jose Lara
A direct proof of the Riesz representation theorem is provided. This theorem characterizes the linear functionals acting on the vector space of continuous functions defined…
Inverse problems for Jacobi operators IV: Interior mass-spring perturbations of semi-infinite systems
Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva
This work gives results on the interplay of the spectra of two Jacobi operators corresponding to an infinite mass-spring system and a modification of it obtained by changing one ma…
Spectral analysis for semi-infinite mass-spring systems
Rafael del Rio, Luis O. Silva
We study how the spectrum of a Jacobi operator changes when this operator is modified by a certain finite rank perturbation. The operator corresponds to an infinite mass-spring sys…
Spectra of Random Operators with absolutely continuous Integrated Density of States
Rafael del Rio
The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empt…
Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems
Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva
Consider an infinite linear mass-spring system and a modification of it obtained by changing the first mass and spring of the system. We give results on the interplay of the spectr…
Inverse problems for Jacobi operators I: Interior mass-spring perturbations in finite systems
Rafael del Rio, Mikhail Kudryavtsev
We consider a linear finite spring mass system which is perturbed by modifying one mass and adding one spring. From knowledge of the natural frequencies of the original and the per…
Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems
Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva
We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruc…
Spectral measures of Jacobi operators with random potentials
Rafael del Rio, Luis O. Silva
Let be a self-adjoint Jacobi operator with a potential sequence of independently distributed random variables with continuous probability distributions and let $…
Spectral averaging techniques for Jacobi matrices
Rafael del Rio, Carmen Martinez, Hermann Schulz-Baldes
Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discu…
Singular continuous spectrum is generic
Rafael del Rio, Svetlana Ya. Jitomirskaya, Nikolai G. Makarov +1
In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spect…