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![https://www.impan.pl/download/pdf/cm118-2-3 [zdalny]](images/mime-icons/pdf.gif "cm118-2-3.pdf")
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Abstrakty
We discuss the spectral properties of the operator
$𝔥_{ℳ }(α) := -d²/dt² + (1/2 t² - α)²$
on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific nilpotent group of a general analysis proposed by J. Dziubański, A. Hulanicki and J. Jenkins.
$𝔥_{ℳ }(α) := -d²/dt² + (1/2 t² - α)²$
on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific nilpotent group of a general analysis proposed by J. Dziubański, A. Hulanicki and J. Jenkins.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
391-400
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Laboratoire de Mathématiques, Université Paris-Sud and CNRS, Bât. 425, F-91405 Orsay Cedex, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-3
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