Generalized eigenfunctions of relativistic Schroedinger operators I

Tomio Umeda

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Generalized eigenfunctions of relativistic Schroedinger operators I

Tomio Umeda

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Abstract

Generalized eigenfunctions of the 3-dimensional relativistic Schrödinger operator $\sqrtΔ + V(x)$ with $|V(x)|\le C < x >^{-σ}$, $σ> 1$, are considered. We show that the generalized eigenfunctions can be expressed as the sum of plane waves and solutions to the time-independent relativistic Schrödinger equation with the radiation condition. If $σ>3$, then we can give pointwise estimates of the differences between the sums and the solutions.

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Tomio Umeda. 2003-10-07. Generalized eigenfunctions of relativistic Schroedinger operators I. https://arxiv.org/abs/math/0310090

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