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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 2, 2009, pp. 233–248
DOI: 10.4171/ZAA/1383

Published online: 2009-06-30

Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces

Erika Tamási[1]

(1) Sapientia University, Cluj-Napoca, Romania

We study the spectral properties of the compact non-negative self-adjoint operator $T=A^{-1}\circ \mathrm{tr}^\Gamma$ acting in the anisotropic Sobolev space $H^{s,a}_2(\rn)$ and give two-sided estimates for the asymptotic behaviour of its eigenvalues $\lambda_k(T)$, where $A$ is a semi-elliptic differential operator of type \[ Au(x)=(-1)^{s_1}\frac{\partial^{2s_1}u(x)}{\partial x_1^{2s_1}} + \cdots + (-1)^{s_n}\frac{\partial^{2s_n}u(x)}{\partial x_n^{2s_n}} + u(x), \] and $\mathrm{tr}^{\Gamma}$ a special trace operator on an anisotropic $d$-set $\Gamma$.

Keywords: Anisotropic function spaces, approximation numbers, semi-elliptic operators, traces

Tamási Erika: Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces. Z. Anal. Anwend. 28 (2009), 233-248. doi: 10.4171/ZAA/1383