We consider a discrete Schrödinger operator 𝒥 with Wigner-von Neumann potential not belonging to l². We find the asymptotics of orthonormal polynomials associated to 𝒥. We prove a Weyl-Titchmarsh type formula, which relates the spectral density of 𝒥 to a coefficient in the asymptotics of the orthonormal polynomials.
The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...
Let be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.
We give a brief survey of recent results of order limited operators related to some properties on Banach lattices.
We improve (in some sense) a recent theorem due to Banas and Knap (1989) about the existence of integrable solutions of a functional-integral equation.
We give a relation between the sign of the mean of an integer-valued, left bounded, random variable and the number of zeros of inside the unit disk, where is the generating function of , under some mild conditions
We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties , , and are not preserved under direct sums of operators. However, we prove that if and are bounded linear operators acting on Banach spaces and having the property , then has the property if and only if , where is the upper semi-B-Weyl spectrum of . We obtain analogous preservation results for the properties , and with...