We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

Hybrid systems, i.e., dynamical systems combining discrete and continuous dynamics, have a complete axiomatization in differential dynamic logic relative to differential equations. Differential invariants are a natural induction principle for proving properties of the remaining differential equations. We study the equational case of differential invariants using a differential operator view. We...

‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products consisting of a scalar function, a homogeneous first order differential operator and the reciprocal of the scalar function. The factorization procedure is utiliz...

The isospectrality problem is studied for the operator of the spherical hydromagnetic α−dynamo. It is shown that this operator is formally pseudo-Hermitian (J−symmetric) and lives in a Krein space. Based on the J−symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the α−dynamo operator matrix. An in...

In this article, we introduce and study two new families of analytic functions by using strong differential subordinations superordinations associated with Wanas operator/. We also give establish some important properties these families.

The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differential geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior algebra...