Bounds for ratios of eigenvalues of the Dirichlet Laplacian
Bounds for ratios of eigenvalues of the Dirichlet Laplacian
We use a doubling scheme to derive a bound for the ratio of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 Superscript k"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{2^k}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>th eigenvalue to the first for the Dirichlet Laplacian on a bounded domain <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" …