Spectral analysis of one class perturbed first order differential operators

a class of fourth order differential operators with transmission conditions

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

Spectral Properties of a Class of Singular Differential Operators

We consider the operator A0f = (−1)n 1 v(t) ( Dρ )∗ [ u(t)Dρ ( f (t) v(t) )] , where Dρ f (t) = dk dtk [ ρ(t) dmf (t) dtm ] , ( Dρ )∗ f (t) = dm dtm [ ρ(t) dkf (t) dtk ] , k + m = n. Our main aim is to prove some spectral properties of a natural extension of this operator. In order to prove this we need to prove some properties of a function space, connected to the operator Dρ , and some embedd...

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS

Spectral Order and Isotonic Differential Operators of Laguerre-pólya Type

Abstract. The spectral order on Rn induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We show that all differential operators of Laguerre-Pólya type preserve the spectral order. We also establish a global monotony property for infinite families of deformations of these operators parametrized by the space l of real bounded sequences. As a consequen...

A FREDHOLM THEORY FOR A CLASS OF FIRST-ORDER ELLIPTIC PARTIAL DIFFERENTIAL OPERATORS IN Rn

The objects of interest are linear first-order elliptic partial differential operators with domain //i(/?" ; C*) in L2(Rn;Ck), the first-order coefficients of which become constant and the zero-order coefficient of which vanishes outside a compact set in R". It is shown that operators of this type are "practically" Fredholm in the following way: Such an operator has a finite index which is inva...