J-self-adjoint extensions of a class of Hamiltonian differential systems

Abstract

Measurements of γ p → K + Λ and γ p → K + Σ 0 cross-sections have been obtained with the photon tagging facility and the Crystal Ball calorimeter at MAMI-C. The measurement uses a novel K + meson identification technique in which the weak decay products are characterized using the energy and timing characteristics of the energy deposit in the calorimeter, a method that has the potential to be applied at many other facilities. The fine center-of-mass energy (W ) resolution and statistical accuracy of the new data results in a significant impact on partial wave analyses aiming to better establish the excitation spectrum of the nucleon. The new analyses disfavor a strong role for quark-diquark dynamics in the nucleon.

Spectra of a class of non-symmetric operators in Hilbert spaces with applications to singular differential operators

“…For a J -symmetric operator T , if S is J -symmetric and T ⊂ S, then S is said to be a J -symmetric extension of T , and if S is J -self-adjoint and it is an extension of T , then S is said to be a J -self-adjoint extension (J -SE) of T . For J -SEs of a J -symmetric operator in H, it has been proved that The definition of the J -GKN-sets for closed J -symmetric operators in H was given in [46] as follows.…”

“…where −∞ < a < b +∞; J is a constant non-singular matrix subjected to J T = −J (A T denotes the transpose of matrix A); W and P are 2n × 2n matrixvalued functions locally integrable on [a, b); W is real-valued with W 0 on [a, b); P T = P ; and λ is a spectral parameter. It was derived in [46] that system (4.1) contains 2n-th order quasi-differential equations with complex coefficients which were studied in [35,36,41]. Introduce the following space:…”

“…There are a number of problems in physics which require the analysis of spectral problems of non-symmetric differential expressions, and then the definition of Jsymmetric operators was introduced by I. M. Glazman [18] in order to study the spectral problems of those non-symmetric differential expressions. For a variety of J -symmetric differential operators, the reader is referred to [7,8,36,41,46]. Unlike symmetric operators, each J -symmetric operator in H has a J -self-adjoint extension (briefly, J -SE) [15].…”

“…Nevertheless, the theory for J -SEs of J -symmetric operators has been studied quite deeply and some elegant results have been obtained [12,15,24,36]. Using them, the characterization of J -SEs for a singular nonsymmetric higher-order differential expression and its general form of the singular J -symmetric Hamiltonian system was given in terms of square-integrable solutions [41,46]. Furthermore, there are many other good results for singular non-symmetric differential expressions (see, e.g., [4, 5, 7-10, 13, 29, 42, 43]).…”

Essential spectra of singular Hamiltonian differential operators of arbitrary order under a class of perturbations

“…In this case, system (1) is said to be (formally)  -symmetric and  * 0 () = () by Ref. [36,Theorem 3.1]. Next, we shall discuss ( 0 ()) and give some properties of it.…”