منابع مشابه
Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian, Rσ(z) := ∑ k (z − λk) σ +. Here {λk} ∞ k=1 are the ordered eigenvalues of the Laplacian on a bounded domain Ω ⊂ Rd, and x+ := max(0, x) denotes the positive part of the quantity x. As corollaries of these inequalities, we derive Weyl-type bounds on λk, on averages such as λ...
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LetΩ be aC2+γ domain in RN ,N ≥ 2, 0 < γ < 1. LetT>0 and let L be a uniformly parabolic operator Lu= ∂u/∂t−∑i, j(∂/∂xi)(ai j(∂u/∂xj)) +∑ j b j(∂u/∂xi) + a0u, a0 ≥ 0, whose coefficients, depending on (x, t) ∈Ω×R, are T periodic in t and satisfy some regularity assumptions. Let A be the N ×N matrix whose i, j entry is ai j and let ν be the unit exterior normal to ∂Ω. Let m be a T-periodic functio...
متن کامل. SP ] 2 4 M ay 2 00 7 Differential inequalities for Riesz means and Weyl - type bounds for eigenvalues 1
We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian, Rσ(z) := ∑ k (z − λk) σ +. Here {λk} ∞ k=1 are the ordered eigenvalues of the Laplacian on a bounded domain Ω ⊂ Rd, and x+ := max(0, x) denotes the positive part of the quantity x. As corollaries of these inequalities, we derive Weyl-type bounds on λk, on averages such as λ...
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We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A + E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantity η = ‖A−1/2EA−1/2‖2, that was already known in the definite case, is shown to be valid as well in the indefinite case. We also extend to the indefinite case relative eigenvector bounds which depend on the same qua...
متن کاملTwo New Weyl-type Bounds for the Dirichlet Laplacian
In this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following lower bounds for its counting function. For λ ≥ λ1, one has N(λ) > 2 n+ 2 1 Hn (λ− λ1) n/2 λ −n/2 1 , and N(λ) > „ n+ 2 n+ 4 «n/2 1 Hn (λ− (1 + 4/n) λ1) n/2 λ −n/2 1 , where Hn = 2 n j2 n/2−1,1 J2 n/2 (jn/2−1,1) is a constant which depends on n, the...
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ژورنال
عنوان ژورنال: Journal of Spectral Theory
سال: 2018
ISSN: 1664-039X
DOI: 10.4171/jst/250