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2 results

  • ON THE RESOLVENT OF THE LAPLACE–BELTRAMI OPERATOR IN HYPERBOLIC SPACE

  • Part of
  • GUSEIN SH. GUSEINOV
  • Journal:
    Journal of the Australian Mathematical Society / Volume 99 / Issue 2 / October 2015
    Published online by Cambridge University Press:
    24 April 2015, pp. 186-206
    Print publication:
    October 2015
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  • In this paper, a detailed description of the resolvent of the Laplace–Beltrami operator in $n$-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green’s function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.

  • Weak Bloch property for discrete magnetic Schrödinger operators

  • Yusuke Higuchi, Tomoyuki Shirai
  • Journal:
    Nagoya Mathematical Journal / Volume 161 / March 2001
    Published online by Cambridge University Press:
    22 January 2016, pp. 127-154
    Print publication:
    March 2001
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  • For a magnetic Schröodinger operator on a graph, which is a generalization of classical Harper operator, we study some spectral properties: the Bloch property and the behaviour of the bottom of the spectrum with respect to magnetic fields. We also show some examples which have interesting properties.