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Reflectionless Discrete Schrödinger Operators are Spectrally Atypical.

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Τίτλος: Reflectionless Discrete Schrödinger Operators are Spectrally Atypical.
Συγγραφείς: VandenBoom, Tom1 tv4@rice.edu
Πηγή: Communications in Mathematical Physics. Apr2018, Vol. 359 Issue 2, p499-514. 16p.
Θεματικοί όροι: *Schrödinger operator, *Spectral sequences (Mathematics), *Hilbert space, *Jacobi operators, *Borel sets
Περίληψη: We prove that, if an isospectral torus contains a discrete Schrödinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schrödinger operator. We also show that the only reflectionless discrete Schrödinger operators having zero, one, or two spectral gaps are periodic. [ABSTRACT FROM AUTHOR]
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  – Url: https://dx.doi.org/doi:10.1007/s00220-017-3068-6
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  Data: Reflectionless Discrete Schrödinger Operators are Spectrally Atypical.
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  Data: <searchLink fieldCode="JN" term="%22Communications+in+Mathematical+Physics%22">Communications in Mathematical Physics</searchLink>. Apr2018, Vol. 359 Issue 2, p499-514. 16p.
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  Data: We prove that, if an isospectral torus contains a discrete Schrödinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schrödinger operator. We also show that the only reflectionless discrete Schrödinger operators having zero, one, or two spectral gaps are periodic. [ABSTRACT FROM AUTHOR]
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        Value: 10.1007/s00220-017-3068-6
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 499
    Subjects:
      – SubjectFull: Schrödinger operator
        Type: general
      – SubjectFull: Spectral sequences (Mathematics)
        Type: general
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Jacobi operators
        Type: general
      – SubjectFull: Borel sets
        Type: general
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      – TitleFull: Reflectionless Discrete Schrödinger Operators are Spectrally Atypical.
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            – D: 15
              M: 04
              Text: Apr2018
              Type: published
              Y: 2018
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              Value: 359
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              Value: 2
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            – TitleFull: Communications in Mathematical Physics
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