Convergence of Padé approximations for a q-hypergeometric series (Wynn's Power Series I).
Density theorems for sampling and interpolation in the Bargmann-Fock space III.
Eigenvalues in the large sieve inequality, II
We explore numerically the eigenvalues of the hermitian formwhen . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Ein Pólyasches Momentenproblem und umhüllende asymptotische Potenzreihen.
Eine lineare Interpolationsaufgabe vom Gontcharoffschen Typ für ganze Funktionen mit Werten in einem komplexen Banachraum.
Equiconvergence of Some Complex Interpolatory Polynomials.
Fejér–Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle
We give a complete characterization of the positive trigonometric polynomials on the bi-circle, which can be factored as where is a polynomial nonzero for and . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities relating...
Finite interpolation on sequences in the disc
This note deals with interpolation of values of analytic functions belonging to a given space, on finite sets of consecutive points of sequences in the disc, performed by rational functions and polynomials. Our goal is to identify sequences and spaces whose functions provide a bound of the error at the first uninterpolated point that is as small as desired. For certain sequences, we prove that this happens for bounded functions, Lipschitz functions and those that have derivatives in the disc algebra....
Free interpolation in Hardy-Orlicz spaces
Gap-interpolation theorems for entire functions.
Generalized interpolation in the unit ball.
We study a generalized interpolation problem for the space H∞(B2) of bounded homomorphic functions in the ball B2. A sequence Z = {zn} of B2 is an interpolating sequence of order 1 if for all sequence of values wn satisfying conditions of order 1 (that is discrete derivatives in the pseudohyperbolic metric are bounded) there exists a function f ∈ H∞(B2) such that f(zn) = wn. These sequences are characterized as unions of 3 free interpolating sequences for H∞(B2) such that all triplets of Z made...
Integral representations for Padé-type operators.
Interpolating sequences and the Nevanlinna Pick problem.
The extremal solutions to the Nevanlinna Pick problem are studied. If there is more than one solution, Nevanlinna showed that all extremal solutions are inner functions. With some extra information on the interpolation data we find that the extremal solutions are Blaschke products whose zeroes form a finite union of interpolating sequences.
Interpolating sequences in the unit ball of
Interpolation and Frames in Certain Banach Spaces of Entire Functions.
Interpolation by multipliers on certain spaces of analytic functions.
Interpolation from a subset of the boundary
Interpolation of bounded sequences
This paper deals with an interpolation problem in the open unit disc of the complex plane. We characterize the sequences in a Stolz angle of , verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on , but very close to the bounded ones. We prove that these interpolating sequences are also uniformly separated, as in the case of the interpolation by bounded holomorphic functions.
Interpolation of entire functions on regular sparse sets and -Taylor series
We give a pure complex variable proof of a theorem by Ismail and Stanton and apply this result in the field of integer-valued entire functions. Our proof rests on a very general interpolation result for entire functions.
Interpolation of infinite order entire functions.