The method of similar operators in the spectral analysis of non-self-adjoint Dirac operators with non-smooth potentials

On spectral properties of Sturm - Liouville operator with matrix potential

“…The main ideas of the similar operators method are presented in the chronological order in works [3]- [7]. We shall follow work [6]. We note that by means of the similar operators method, the spectral properties of various differential operators were studied, for instance, in works [8]- [11], [16].…”

“…If ∈ ( ), it follows from (9) and (10) that the action of operators and Γ on a vector is introduced in the same way as in Definition 2 and they are used in Theorem 3. Such transformation is possible under the validity of the following assumption [6], [12].…”

“…This is why sometimes it is convenient to make a preliminary similarity transformation of operator − into operator −̃︀, wherẽ︀ ∈ ℳ ( / ∈ ℳ). Continuations of transformers and Γ on space L (ℋ) are denoted by the same symbols and is made by as follows (see [6]). Let 0 ∈ ( ) and…”

The Completeness of System of Eigenfunctions of 1D Dirac Operators

“…Moreover, explicit conditions of the dissipativity and completeness of such operators were found. It is also worth to mention recent papers [5]- [9] devoted to the Riesz basis property for 22  Dirac operator (see also references therein).…”

Bir Boyutlu Dirac Operatörlerinin Özfonksiyonlar Sisteminin Tamlığı

“…Moreover, explicit conditions of the dissipativity and completeness of such operators were found. It is also worth to mention recent papers [5]- [9] devoted to the Riesz basis property for 22  Dirac operator (see also references therein).…”