Five integral inequalities; an inheritance from Hardy and Littlewood.
Floquet operators with singular spectrum. III
Formally normal ordinary differential operators
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval
In this paper we consider a linear operator on an unbounded interval associated with a matrix linear Hamiltonian system. We characterize its Friedrichs extension in terms of the recessive system of solutions at infinity. This generalizes a similar result obtained by Marletta and Zettl for linear operators defined by even order Sturm-Liouville differential equations.
Fučík spectra for vector equations.
Geometric aspects of higher-order eigenvalue problems. I: Structures on spaces of boundary conditions.
Hardy type inequalities for integral transforms associated with a singular second order differential operator.
Identification of a wave equation generated by a string
We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.
Inequalities among eigenvalues of Sturm-Liouville problems.
Inequalities for eigenvalue functionals.
Inverse problems on star-type graphs: differential operators of different orders on different edges
We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.
Isospectral Sets for AKNS Systems on the Unit Interval with Generalized Periodic Boundary Conditions.
Le problème spectral inverse pour les systèmes AKNS périodiques sur la droite réelle
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Nonhermitian systems and pseudospectra
Four applications are outlined of pseudospectra of highly nonnormal linear operators.
Non-self-adjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter.
On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane
∗ Partially supported by Grant MM-428/94 of MESC.Systems of orthogonal polynomials on the real line play an important role in the theory of special functions [1]. They find applications in numerous problems of mathematical physics and classical analysis. It is known, that classical polynomials have a number of properties, which uniquely define them.
On discreteness of spectrum of a functional differential operator
We study conditions of discreteness of spectrum of the functional-differential operator on . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
On Floquet eigenvalue problems for first order differential systems in the complex domain.
On nonresonance problems of second-order difference systems.