On spectral measures of strings and excursions of quasi-diffusions
On the basis properties of a spectral problem with a spectral parameter in a boundary condition.
On the basis property of the root functions of differential operators with matrix coefficients
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.
On the canonical development of Parseval formulas for singular differential operators
Per funzioni opportune si ottiene una formula di Parseval per operatori differenziali singolari di tipo dell'operatore radiale di Laplace-Beltrami. è una funzione spettrale generalizzata di tipo Marčenko e può essere rappresentata per mezzo di un certo nucleo della trasmutazione.
On the completeness of eigenfunctions and associated functions of irregular multipoint eigenvalue-problems.
On the convergence of biorthogonal series corresponding to nonselfadjoint Sturm-Liouville operator with discontinuous coefficients.
On the convergence of expansions with respect to eigen-and adjoint functions of a non-self-adjoint Sturm-Liouville type operator with discontinuous coefficients.
On the differential form spectrum of hyperbolic manifolds
We give a lower bound for the bottom of the differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.
On the differential operators with periodic matrix coefficients.
On the discreteness of the spectra of the Dirichlet and Neumann -biharmonic problems.
On the Eigenvalues of Nonselfadjoint Problems Involving Indefinite Weights.
On the essential spectra of matrix operators and applications.
On the essential spectrum of Dirac operators with spherically symmetric potentials.
On the Expansion Theorem for a Certain Boundary Value Problem for a Functional Differential Equation
On the genericity of nonvanishing instability intervals in Hills equation
On the genericity of nonvanishing instability intervals in periodic Dirac systems
On the growth of the spectral measure.
On the isospectral beams.
On the -solutions to general second-order nonsymmetric differential equations.
On the Lyapunov exponent and exponential dichotomy for the quasi-periodic Schrödinger operator
In this paper we study the Lyapunov exponent for the one-dimensional Schrödinger operator with a quasi-periodic potential. Let be the set of frequency vectors whose components are rationally independent. Let , and consider the complement in of the set where exponential dichotomy holds. We show that is generic in this complement. The methods and techniques used are based on the concepts of rotation number and exponential dichotomy.