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On the Weyl solution of the 1-dim Schrödinger operator with inverse fourth power potential

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Abstract

We consider the one dimensional Schrödinger operator with potential \(1/x^4\) on the half line. It is known that a generalized Titchmarsh–Weyl function can be associated to it. For other strongly singular potentials in some previous works it was possible to give an operator theoretic interpretation of this fact. However, for the present potential we show that such an interpretation does not exist.

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Acknowledgments

We are grateful to Fritz Gesztesy for pointing out the reference [24] that directed us in the right direction. Moreover, we thank the Institute Mittag-Leffler for its hospitality during the workshop “Modern aspects of the Titchmarsh–Weyl m-function and its multidimensional analogues” in June 2014, including access to the library.

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  1. Stockholm, Sweden

    Annemarie Luger & Christoph Neuner

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  1. Annemarie Luger
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  2. Christoph Neuner
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Correspondence to Christoph Neuner.

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Communicated by G. Teschl.

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Luger, A., Neuner, C. On the Weyl solution of the 1-dim Schrödinger operator with inverse fourth power potential. Monatsh Math 180, 295–303 (2016). https://doi.org/10.1007/s00605-015-0826-4

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