Eigenvalue distribution of some fractal semi-elliptic differential operators

Eigenvalue distribution of some fractal semi-elliptic differential operators

We consider differential operators of type Au(x) = u(x) + (−1)t1 ∂ 2t1u(x) ∂x1 1 + (−1)t2 ∂ 2t2u(x) ∂x2 2 , x = (x1, x2) ∈ R2, and Sierpinski carpets Γ ⊂ R2. The aim of the paper is to investigate spectral properties of the fractal differential operator A−1 ◦ trΓ acting in the anisotropic Sobolev space W (t1,t2) 2 (R 2) where trΓ is closely related to the trace operator trΓ . Mathematics Subjec...

Interpolation methods to estimate eigenvalue distribution of some integral operators

We study the asymptotic distribution of eigenvalues of integral operators Tk defined by kernels k which belong to Triebel-Lizorkin function space Fσ pu(F qv) by using the factorization theorem and the Weyl numbers xn. We use the relation between Triebel-Lizorkin space Fσ pu(Ω) and Besov space Bτ pq(Ω) and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizo...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Adaptive Eigenvalue Computation for Elliptic Operators

This article is concerned with recent developments of adaptive wavelet solvers for elliptic eigenvalue problems. We describe the underlying abstract iteration scheme of the preconditioned perturbed iteration. We apply the iteration to a simple model problem in order to identify the main ideas which a numerical realization of the abstract scheme is based upon. This indicates how these concepts c...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators