Eigenvalue Decay of Operators on Harmonic Function Spaces
نویسنده
چکیده
Let Ω be an open set in R (d > 1) and h(Ω) the Fréchet space of harmonic functions on Ω. Given a bounded linear operator L : h(Ω) → h(Ω), we show that its eigenvalues λn, arranged in decreasing order and counting multiplicities, satisfy |λn| ≤ K exp(−cn ), where K and c are two explicitly computable positive constants.
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[4] D. Haroske. Some logarithmic function spaces, entropy numbers, applications to spectral theory. [9] D. Haroske and H. Triebel. Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential operators I. [10] D. Haroske and H. Triebel. Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential o...
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