On index theory for non-Fredholm operators: A (1 + 1)-dimensional example
Using the general formalism of , a study of index theory for non-Fredholm operators was initiated in . Natural examples arise from (1 + 1)-dimensional differential operators using the model operator DA in L2(R2; dtdx) of the type DA = d dt + A, where A = ´ ⊕ R dtA(t), and the family of self-adjoint operators A(t) in L2(R; dx) studied here is explicitly given by A(t) = −i d dx + θ(t)φ(·), t ∈ R. Here φ : R → R has to be integrable on R and θ : R → R tends to zero as t → −∞ and to 1 as...[Show more]
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