On spectral properties of one class difference operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Spectral Properties of a Class of Reflectionless Schrödinger Operators

We prove that one-dimensional reflectionless Schrödinger operators with spectrum a homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and Yuditskii, have purely absolutely continuous spectra. This class includes all earlier examples of reflectionless almost periodic Schrödinger operators. In addition, we construct examples of reflectionless Schrödinger operator...

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...

Unusual spectral properties of a class of Schrödinger operators

Spectral Properties of a Certain Class of Carleman Operators

The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L (X,μ) and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula. 1. Preliminaries The set of generalized r...