The indefinite Sturm-Liouville operator A = (sgnx)(−d2/dx2 + q(x)) is studied. It is proved that similarity of A to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components Aess and Adisc of A corresponding to essential and discrete spectrums, respec...

The indefinite Sturm-Liouville operator A = (sgnx)(−d2/dx2 + q(x)) is studied. It is proved that similarity of A to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components Aess and Adisc of A corresponding to essential and discrete spectrums, respec...

Boundary value problems involving oblique or mixed second derivative boundary conditions[ I, 31 arise in the description of heat (or mass) transfer in stationary media which are peripherally cooled (or leached) by a fluid in which the temperature (or concentration) is varying significantly in the direction of flow. By decomposing the energy equation into a pair of first order systems Ramkrishna...

The paper continues the study of differential Banach *algebras AS and FS of operators associated with symmetric operators S on Hilbert spaces H. The algebra AS is the domain of the largest *-derivation δS of B(H) implemented by S and the algebra FS is the closure of the set of all finite rank operators in AS with respect to the norm ‖A‖ = ‖A‖+‖δS(A)‖. When S is selfadjoint, FS is the domain of ...

Classical orthogonal polynomials and matrix polynomials being orthogonal with respect to some Hermitean positive deenite matrix of measures share several properties , e.g., three term recurrencies, Christooel{Darboux formulas; there are connections to the triangular decomposition of the (inverse) moment matrix and to eigenvalue{problems for the banded matrix of recurrence coeecients. Also, a co...