منابع مشابه
Scattering Matrix and Functions of Self-adjoint Operators
In the scattering theory framework, we consider a pair of operators H0, H. For a continuous function φ vanishing at infinity, we set φδ(·) = φ(·/δ) and study the spectrum of the difference φδ(H − λ)− φδ(H0 − λ) for δ → 0. We prove that if λ is in the absolutely continuous spectrum of H0 and H, then the spectrum of this difference converges to a set that can be explicitly described in terms of (...
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Let V and W be real or complex finite dimensional vector spaces with inner products 〈·, ·〉V and 〈·, ·〉W , respectively. Let L : V → W be linear. If there is a transformation L∗ : W → V for which 〈Lv,w〉W = 〈v, Lw〉V (1) holds for every pair of vectors v ∈ V and w in W , then L∗ is said to be the adjoint of L. Some of the properties of L∗ are listed below. Proposition 1.1. Let L : V →W be linear. ...
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ژورنال
عنوان ژورنال: Journal of Spectral Theory
سال: 2011
ISSN: 1664-039X
DOI: 10.4171/jst/10