Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach

K. Naimark; M. Solomyak

doi:10.1007/BF01198143

Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach

K. Naimark^*
, M. Solomyak

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We obtain the sharp order of growth of the eigenvalue distribution function for the operator in the anisotropic Sobolev space H^t1, ^t2(Q), generated by the quadratic form (latin small letter esh)_Q\u\²dμ, where Q ⊂ ℝ² is the unit square and μ is a probability self-affine fractal measure on Q. The geometry of Supp μ should be in a certain way consistent with the parameters t₁, t₂.

Original language	English
Pages (from-to)	495-506
Number of pages	12
Journal	Integral Equations and Operator Theory
Volume	40
Issue number	4
DOIs	https://doi.org/10.1007/BF01198143
State	Published - 2001
Externally published	Yes

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AB - We obtain the sharp order of growth of the eigenvalue distribution function for the operator in the anisotropic Sobolev space Ht1, t2(Q), generated by the quadratic form (latin small letter esh)Q\u\2dμ, where Q ⊂ ℝ2 is the unit square and μ is a probability self-affine fractal measure on Q. The geometry of Supp μ should be in a certain way consistent with the parameters t1, t2.

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -

Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach

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