Optimal Quadrature of Hp Functions.
Outer and inner vanishing measures and division in H∞ + C.
Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in H∞ + C. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in H∞ + C.
Outers for noncommutative revisited
We continue our study of outer elements of the noncommutative spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ ∈ Ball(A)...