Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach |
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Authors: | K Naimark M Solomyak |
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Institution: | (1) Department of Mathematics, The Weizmann Institute of Science, 76100 Rehovot, Israel |
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Abstract: | We obtain the sharp order of growth of the eigenvalue distribution function for the operator in the anisotropic Sobolev space
, generated by the quadratic form
Q
u 2
d , whereQ![sub](/content/l11u024584205222/xxlarge8834.gif) 2 is the unit square and is a probability self-affine fractal measure onQ. The geometry of Supp should be in a certain way consistent with the parameterst
1
,t
2
. |
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Keywords: | 35P15 28A80 |
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