GENERALIZED EIGENFUNCTIONS OF RELATIVISTIC SCHRODINGER OPERATORS IN TWO DIMENSIONS

被引：0

作者：

Umeda, Tomio ^{[1
]}

Wei, Dabi ^{[2
]}

机构：

[1] Univ Hyogo, Dept Math Sci, Himeji, Hyogo 6712201, Japan

[2] Tokyo Inst Technol, Dept Mech & Control Engn, Grad Sch Sci & Engn, Meguro Ku, Tokyo 1528550, Japan

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年

基金：

日本学术振兴会;

关键词：

Relativistic Schrodinger operators; generalized eigenfunctions; pseudo-relativistic Hamiltonians;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article concerns the generalized eigenfunctions of the two-dimensional relativistic Schrodinger operator H = root-Delta + V(x) with vertical bar V(x)vertical bar <= C < x >(-sigma), sigma > 3/2. We compute the integral kernels of the boundary values R-0(+/-)(lambda) = (root-Delta - (lambda +/- i0))(-1), and prove that the generalized eigenfunctions phi(+/-)(x, k) are bounded on R-x(2) x {k : a <= vertical bar k vertical bar <= b}, where [a, b] subset of (0, infinity)\sigma(p)(H), and sigma(p)(H) is the set of eigenvalues of H. With this fact and the completeness of the wave operators, we establish the eigenfunction expansion for the absolutely continuous subspace for H. Finally, we show that each generalized eigenfunction is asymptotically equal to a sum of a plane wave and a spherical wave under the assumption that sigma > 2.

引用

页数：18