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- Kristian Seip
- 2008

We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von Neumann lattice, and similarly, a discrete set is a set of interpolation if andâ€¦ (More)

- ME T HODS, Brynjulf Owren, Kristian Seip
- 1990

The theory of positive real functions is used to provide bounds for the largest possible disk to be inscribed in the stability region of an explicit Runge-Kutta method. In particular, we show that the closed disk 1~ + rl < r can be contained in the stability region of an explicit m-stage Runge-Kutta method of order two if and only if r _< m 1. AMSâ€¦ (More)

- Peder A. Olsen, Kristian Seip
- IEEE Trans. Information Theory
- 1992

An analogue of the notion of uniformly separated sequences, expressed in terms of canonical divisors, is shown to yield a necessary and sufficient condition for interpolation in the Bergman space Ap, 0 < p < âˆž. A sequence Î“ = {zj} of distinct points in the open unit disk D = {z : |z| < 1} of the complex plane is a classical interpolation sequence if forâ€¦ (More)

- Kristian Seip
- IEEE Trans. Information Theory
- 1990

A formula is given for the completeness radius of a random exponential system {tleiÎ¾nt}pnâˆ’1 l=0,nâˆˆZ in terms of the probability measures of Î¾n. The purpose of this note is to formulate a probabilistic version of the celebrated Beurling-Malliavin theorem on the completeness radius of a sequence of complex exponentials [1]. First, to state theâ€¦ (More)

The set of realizable refractive indices as a function of frequency is considered. For passive media we give bounds for the refractive index variation in a finite bandwidth. Special attention is given to the loss and index variation in the case of left-handed materials.

An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when 0 < p â‰¤ 1, of Fock-type when 0 < p â‰¤ 2, and of Bergman-type when 0 < p < âˆž. Moreover, if a uniformly discrete sequence has aâ€¦ (More)

The upper and lower uniform densities of some regular sequences are computed. These densities are used to determine sets of sampling and interpolation for Bergman spaces of the unit disk. Â§

- Artur Nicolau, Joaquim Ortega-CerdÃ , Kristian Seip, Peter Jones
- 2003

We prove that a suitably adjusted version of Peter Jonesâ€™ formula for interpolation in Hâˆž gives a sharp upper bound for what is known as the constant of interpolation. We show how this leads to precise and computable numerical bounds for this constant. With each finite or infinite sequence Z = (zj) (j = 1, 2, ...) of distinct points zj = xj + iyj in theâ€¦ (More)