1,947 research outputs found
Spectral bounds for singular indefinite Sturm-Liouville operators with --potentials
The spectrum of the singular indefinite Sturm-Liouville operator
with a real
potential covers the whole real line and, in addition,
non-real eigenvalues may appear if the potential assumes negative values. A
quantitative analysis of the non-real eigenvalues is a challenging problem, and
so far only partial results in this direction were obtained. In this paper the
bound on the absolute values of the non-real
eigenvalues of is obtained. Furthermore, separate bounds on the
imaginary parts and absolute values of these eigenvalues are proved in terms of
the -norm of the negative part of .Comment: to appear in Proc. Amer. Math. So
The non-real spectrum of a singular indefinite Sturm-Liouville operator with regular left endpoint
PT-Symmetric Hamiltonians as couplings of dual pairs
In the seminal paper (Bender & Boettcher, 1998) a new view of quantum mechanics was proposed. This new view differs from the old one in that the restriction on the Hamiltonian to be Hermitian is relaxed: now the Hamiltonian is PT -symmetric. Here P is parity and T is time reversal. Since 1998, PT -symmetric Hamiltonians have been analyzed intensively by many authors. In Mostafazadeh (2002) PT -symmetry was embedded into the more general mathematical framework of pseudo-Hermiticity or, what is the same, self-adjoint operators in Kre˘ın spaces, see (Langer & Tretter, 2004; Azizov & Trunk, 2012; Hassi & Kuzhel, 2013; Leben & Trunk, 2019). For a general introduction to PT -symmetric quantum mechanics we refer to the overview paper of Mostafazadeh (2010) and to the books of Moiseyev (2011) and Bender (2019)
Interfacing Models for Thermal Separation Processes with Fluid Property Data from External Sources
Relative oscillation theory and essential spectra of Sturm--Liouville operators
We develop relative oscillation theory for general Sturm-Liouville
differential expressions of the form and prove perturbation results and invariance of essential
spectra in terms of the real coefficients , , . The novelty here is
that we also allow perturbations of the weight function in which case the
unperturbed and the perturbed operator act in different Hilbert spaces.Comment: 15 page
Relative oscillation theory and essential spectra of Sturm-Liouville operators
We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form 1/r(-d/dx p d/dx + q) and prove perturbation results and invariance of essential spectra in terms of the real coefficients p, q, r. The novelty here is that we also allow perturbations of the weight function r in which case the unperturbed and the perturbed operator act in different Hilbert spaces
Lower bounds for self-adjoint Sturm-Liouville operators
The numerical range and the quadratic numerical range is used to study the spectrum of a class of block operator matrices. We show that the approximate point spectrum is contained in the closure of the quadratic numerical range. In particular, the spectral enclosures yield a spectral gap. It is shown that these spectral bounds are tighter than classical numerical range bounds
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