Generalized Eigenfunctions for Dirac Operators Near Criticality
نویسنده
چکیده
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. We also estimate the k-derivatives which are important for estimating decay. The method also applies for other differential operators (for example Schrödinger operators). ∗Institut für theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria E-mail: [email protected]
منابع مشابه
Generalized Eigenfunctions for critical potentials with small perturbations
We estimate the behavior of the generalized eigenfunctions of critical Dirac operators (which are Dirac operators with eigenfunctions and/or resonances for E = m) under small perturbations in the potential. The results also apply for other differential operators (for example Schrödinger operators).
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