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Absolutely continuous spectrum and scattering in the surface Maryland model

François Bentosela, Philippe Briet, Leonid Pastur (2001)

Journées équations aux dérivées partielles

We study the discrete Schrödinger operator H in 𝐙 d with the surface quasi periodic potential V ( x ) = g δ ( x 1 ) tan π ( α · x 2 + ω ) , where x = ( x 1 , x 2 ) , x 1 ∈ 𝐙 d 1 , x 2 ∈ 𝐙 d 2 , α ∈ 𝐑 d 2 , ω ∈ [ 0 , 1 ) . We first discuss a proof of the pure absolute continuity of the spectrum of H on the interval [ - d , d ] (the spectrum of the discrete laplacian) in the case where the components of α are rationally independent. Then we show that in this case the generalized eigenfunctions have the form of the “volume” waves, i.e. of the sum of the incident plane wave and reflected from the hyper-plane 𝐙 d 1 waves, the form...

Absolutely (r,p,q)-summing inclusions

Carsten Michels (2007)

Studia Mathematica

As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary...

Absolutely Summing Terraced Matrices

Ibrahim Almasri (2016)

Concrete Operators

Let α > 0. By Cα we mean the terraced matrix defined by [...] if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be [...] in the region 1/p + 1/q ≤ 1.

Currently displaying 861 – 880 of 1501