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On index theory for non-Fredholm operators: A (1 + 1)-dimensional example

Carey, Alan; Gesztesy, Fritz; Levitina, Galina; Potapov, Denis; Sukochev, Fedor A; Zanin, Dima

Description

Using the general formalism of [12], a study of index theory for non-Fredholm operators was initiated in [9]. 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]

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
URI: http://hdl.handle.net/1885/103597
Source: Mathematische Nachrichten
DOI: 10.1002/mana.201500065

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