Generalized eigenfunctions for Dirac operators near criticality
نویسندگان
چکیده
منابع مشابه
Generalized Eigenfunctions for Dirac Operators Near Criticality
Critical Dirac operators are those which have eigenfunctions and/or resonances for E = m. We estimate the behavior of the generalized eigenfunctions of critical Dirac operators under small perturbations of the potential. The estimates are done in the L∞-norm. We show that for small k the generalized eigenfunctions are in leading order multiples of the respective eigenfunctions and/or resonances...
متن کاملGeneralized eigenfunctions of relativistic Schrödinger operators I
Generalized eigenfunctions of the 3-dimensional relativistic Schrödinger operator √ ∆+ V (x) with |V (x)| ≤ C〈x〉−σ, σ > 1, are considered. We construct the generalized eigenfunctions by exploiting results on the limiting absorption principle. We compute explicitly the integral kernel of ( √ −∆ − z), z ∈ C \ [0, +∞), which has nothing in common with the integral kernel of (−∆− z), but the leadin...
متن کاملEigenfunctions of Dirac Operators at the Threshold Energies
We show that the eigenspaces of the Dirac operator H = α · (D − A(x)) + mβ at the threshold energies ±m are coincide with the direct sum of the zero space and the kernel of the Weyl-Dirac operator σ·(D−A(x)). Based on this result, we describe the asymptotic limits of the eigenfunctions of the Dirac operator corresponding to these threshold energies. Also, we discuss the set of vector potentials...
متن کاملEigenfunctions at the Threshold Energies of Magnetic Dirac Operators
We propose a simple proof of characterization of the eigenspaces corresponding to the eigenvalues ±m of a supersymmetric Dirac operatorH = Q+mτ , where Q is a supercharge, m a positive constant, and τ the unitary involution. The proof is abstract, but not relevant to the abstract Foldy-Wouthuysen transformation. We then apply the obtained results to magnetic Dirac operators, and derive a series...
متن کاملGeneralized Continuous Frames for Operators
In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2809265