Singularities of Generalized Strings

Kaltenbäck, Michael; Winkler, Henrik; Woracek, Harald

doi:10.1007/3-7643-7516-7_9

Cited by 13 publications

(8 citation statements)

References 9 publications

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“…[WW], it is much more suitable to work with Hamiltonians which may vanish on sets of positive measure. Especially when working with transformation formulas like those introduced in [KWW1], dropping the requirement that Hamiltonians are non-vanishing is very helpful.…”

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confidence: 99%

Reparametrizations of Non Trace-normed Hamiltonians

Winkler

Woracek

2012

Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

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We consider a Hamiltonian system of the form y (x) = JH(x)y(x), with a locally integrable and nonnegative 2 × 2-matrix valued Hamiltonian H(x). In the literature dealing with the operator theory of such equations, it is often required in addition that the Hamiltonian H is trace-normed, i.e. satisfies tr H(x) ≡ 1. However, in many examples this property does not hold. The general idea is that one can reduce to the trace-normed case by applying a suitable change of scale (reparametrization). In this paper we justify this idea and work out the notion of reparametrization in detail.

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confidence: 99%

Reparametrizations of Non Trace-normed Hamiltonians

Winkler

Woracek

2012

Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

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“…Since the poles of W ⋆ cot φ(s + ) interlace with the poles of W ⋆∞, the right lower entry of W has at most one pole on (−∞, 0). An application of [KWW1,Proposition 3.12] yields that the order of W cannot exceed 1/2. It follows that H has the property S p whenever p > 1/2.…”

Section: Compactness Propertiesmentioning

confidence: 99%

A growth condition for Hamiltonian systems related with Kreĭn strings

Winkler¹,

Woracek²

2014

Acta Sci. Math.

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“…Various subclasses of Nevanlinna functions have been studied in the past, e.g., Kac, Stieltjes, and inverse Stieltjes functions in connection with spectral problems for strings; cf. [7,[17][18][19][20][21]23,24] and [3,[8][9][10]15].…”

Section: Introductionmentioning

confidence: 99%