\(L^p\)-boundedness of wave operators for 2D Schrödinger operators with point interactions

Author name not available (Why is that?)

Abstract: For two dimensional Schr"odinger operator

H

with point interactions, We prove that wave operators of scattering for the pair

(H, H_{0})

,

H_{0}

being the free Schr"odinger operator, are bounded in the Lebesgue space

L^{p} (R^{2})

for

1 < p < i n f t y

if and only if there are no generalized eigenfunctions of

H u (x) = 0

which satisfy

u (x) = C | x |^{- 1} + o (| x |^{- 1})

as

| x | o i n f t y

,

C o t = 0

. Otherwise they are bounded for

1 < p l e q 2

and unbounded for

2 < p < i n f t y

.

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