A characterization of the complex affine line.
A counterexample to the Γ-interpolation conjecture
Agler, Lykova and Young introduced a sequence , where ν ≥ 0, of necessary conditions for the solvability of the finite interpolation problem for analytic functions from the open unit disc into the symmetrized bidisc Γ. They conjectured that condition is necessary and sufficient for the solvability of an n-point interpolation problem. The aim of this article is to give a counterexample to that conjecture.
A notion of extremal analytic discs related to interpolation in the ball.
A reducibility problem for the classical residue formula
A singular controllability problem with vanishing viscosity
The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? The characteristic of our viscous term is that it contains the fractional power α of the Dirichlet Laplace operator. Through the parameter α we may increase or decrease the strength of the high frequencies damping which allows us to cover a large class of dissipative mechanisms. The viscous term,...
A weighted interpolation problem for analytic functions
An example concerning analytic functions with finite Dirichlet integrals
An explicit interpolation formula for the Hardy space.
An observation on the Turán-Nazarov inequality
The main observation of this note is that the Lebesgue measure μ in the Turán-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant ω ≥ μ, which can be effectively estimated in terms of the metric entropy of a set, and may be nonzero for discrete and even finite sets. While the frequencies (the imaginary parts of the exponents) do not enter the original Turán-Nazarov inequality, they necessarily enter the definition of ω.
Analytic interpolation and the degree constraint
Analytic interpolation problems arise quite naturally in a variety of engineering applications. This is due to the fact that analyticity of a (transfer) function relates to the stability of a corresponding dynamical system, while positive realness and contractiveness relate to passivity. On the other hand, the degree of an interpolant relates to the dimension of the pertinent system, and this motivates our interest in constraining the degree of interpolants. The purpose of the present paper is to...
Approximation and interpolation of entire functions and generalized orders
Bargmann representation of q-commutation relations for q > 1 and associated measures
The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product . We consider the problem of representing the functional F as a measure for q > 1. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.
Beurling type density theorems in the unit disk.
Characterization of linear functionals associated with bilinear forms of Sobolev type.
Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's (Ap) condition.
We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 < p < ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...
Continued Fractions Associated With the Newton-Padé Table.
Continuity and convergence properties of extremal interpolating disks.
Let a be a sequence of points in the unit ball of Cn. Eric Amar and the author have introduced the nonnegative quantity ρ(a) = infα infk Πj:j≠k dG(αj, αk), where dG is the Gleason distance in the unit disk and the first infimum is taken over all sequences α in the unit disk which map to a by a map from the disk to the ball.The value of ρ(a) is related to whether a is an interpolating sequence with respect to analytic disks passing through it, and if a is an interpolating sequence in the ball, then...
Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III).
Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III). (Summary).
Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series I). (Summary).