Abstract
Let H be a Banach space of all complex sequences h=(h 1,h 2, …), hj ∈ C, equipped with the norm
We introduce the Banach space H 1 which is the space of all vector functions u(x)=(u 1(x), u 2(x), …), x∈ Rn (uj ∈ L 1(Rn ), j=1,2, …) that has a range in H, equipped with the norm
In this article we study the separation of the Schrodinger-type operator A= − P +V(x), x∈ Rn , in the Banach space H 1, with the linear operator potential V(x). Moreover, we study the separation of the nonlinear Schrodinger-type operator B= − P+V(x,h), x∈ Rn , h∈ H, in the Banach space H 1, with the nonlinear operator potential V(x,h), where
with real valued functions b k (x) and akr (x) in C 1(Rn ), and
Notes
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Email: [email protected]
Email: [email protected]