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On the spectrum of the Neumann Laplacian of long-range horns: a note on the Davies-Simon theorem

On the spectrum of the Neumann Laplacian of long-range horns: a note on the Davies-Simon theorem

For a class of regions with cusps (e.g., <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega equals left-brace left-parenthesis x comma y right-parenthesis colon x greater-than 1 comma StartAbsoluteValue y EndAbsoluteValue greater-than exp left-parenthesis minus x Superscript alpha Baseline right-parenthesis right-brace comma 0 greater-than alpha greater-than 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi …