Journal of Mathematics
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Research Reports on Functional Analysis from Chalmers University of Technology Provide New Insights
July 5th, 2011
According to the authors of recent research from Gothenburg, Sweden, "The behavior of the discrete spectrum of the Schrodinger operator -Delta - V is determined to a large extent by the behavior of the corresponding heat kernel P(t; x, y) as t -> 0 and t -> infinity. If this behavior is power-like, i.e., parallel to P(t; .,.)parallel to(L)infinity = O(t(-delta/2)), t -> 0, parallel to P(t; .,)parallel to(L)infinity = O(t-(D/2)), t -> infinity, then it is natural to call the exponents delta and D the local dimension and the dimension at infinity, respectively."
"The character of spectral estimates depends on a relation between these dimensions. The case where delta < D,...
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Source: Journal of Mathematics (2011-07-05)