Spectral Aspects of the Skew-Shift Operator: A Numerical Perspective
نویسندگان
چکیده
منابع مشابه
The Spectral Shift Operator
We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz functions and their logarithms. Applications to Krein's trace formula and to the Birman-Solomyak spectral averaging formula are discussed.
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The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its operator-valued extension, and an abstract approach to trace formulas based on perturbation theory and the theory of self-adjoint extensions of symmetric opera...
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For a large class of admissible functions f : R 7→ C, the operator derivatives dj dxj f(H0 + xV ), where H0 and V are self-adjoint operators on a separable Hilbert space H, exist and can be represented as multiple operator integrals [1, 14]. Let M be a semi-finite von Neumann algebra acting on H and τ a semi-finite normal faithful trace on M. For H0 = H ∗ 0 affiliated with M and V = V ∗ in the ...
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The Lifshits–Krein spectral shift function is considered for the pair of operators H0 = (−4)l, l > 0 and H = H0 + V in L2(R), d ≥ 1; here V is a multiplication operator. The estimates for this spectral shift function ξ(λ;H,H0) are obtained in terms of the spectral parameter λ > 0 and the integral norms of V . These estimates are in a good agreement with the ones predicted by the classical phase...
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let $g$ be a simple graph, and $g^{sigma}$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^{sigma})$. the $k-$th skew spectral moment of $g^{sigma}$, denoted by $t_k(g^{sigma})$, is defined as $sum_{i=1}^{n}( lambda_{i})^{k}$, where $lambda_{1}, lambda_{2},cdots, lambda_{n}$ are the eigenvalues of $g^{sigma}$. suppose $g^{sigma...
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ژورنال
عنوان ژورنال: Communications in Computational Physics
سال: 2014
ISSN: 1815-2406,1991-7120
DOI: 10.4208/cicp.120513.290813a