Electron. J. Diff. Eqns.,
Vol. 2006(2006), No. 127, pp. 146.
Generalized eigenfunctions of relativistic
Schrodinger operators I
Tomio Umeda
Abstract:
Generalized eigenfunctions of the 3dimensional relativistic
Schrodinger operator
with
,
,
are considered. We construct the generalized eigenfunctions
by exploiting results on the limiting absorption principle.
We compute explicitly the integral kernel of
,
,
which has nothing in common with
the integral kernel of
,
but the leading term of the integral kernels of the boundary
values
,
,
turn out to be the same, up to a constant, as the integral
kernels of the boundary values
.
This fact enables us to show that
the asymptotic behavior, as
, of
the generalized eigenfunction of
is equal to
the sum of a plane wave and a spherical wave when
.
Submitted September 22, 2006. Published October 11, 2006.
Math Subject Classifications: 35P99, 35S99, 47G30, 47A40.
Key Words: Relativistic Schrodinger operators; pseudorelativistic
Hamiltonians; generalized eigenfunctions; Riesz potentials;
radiation conditions.
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Tomio Umeda
Department of Mathematical Sciences
University of Hyogo
Shosha, Himeji 6712201, Japan
Telephone +81792674935 Fax +81792668868
email: umeda@sci.uhyogo.ac.jp 
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