Related papers: Sampling and interpolation in de Branges spaces wi…
We give analytic description for the completion of $C_0^\infty ( \mathbf{R}_+)$ in Dirichlet space $D^{1,p}(\mathbf{R}_+, \omega):= \{ u:\mathbf{R}_+\rightarrow \mathbf{R}: u\ \hbox{ is locally absolutely continuous on} \ \mathbf{R}_+ \…
Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in…
We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the…
We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…
We define $(\alpha_n)$ -regular sets in uniformly perfect metric spaces. This definition is quasisymmetrically invariant and the construction resembles generalized dyadic cubes in metric spaces. For these sets we then determine the…
The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$,…
We prove two theorems of Paley and Wiener in the slice regular setting. As an application, we can compute the reproducing kernel for the slice regular Paley-Wiener space, and obtain a related sampling theorem.
We introduce a new, simple metric method of sampling metric measure spaces, based on a well-known "snowflakeing operator" and we show that, as a consequence of a classical result of Assouad, the sampling of doubling metric spaces is…
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale.…
We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that the doubling constant of the measure can be chosen to be…
The complex method of interpolation, going back to Calder\'on and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of…
Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations…
We consider Dirichlet spaces with superharmonic weights. This class contains both the harmonic weights and the power weights. Our main result is a characterization of the Dirichlet spaces with superharmonic weights that can be identified as…
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a…
We modify the classical Paley-Wiener spaces $PW_x$ of entire functions of finite exponential type at most $x>0$, which are square integrable on the real line, via the additional condition of vanishing at finitely many complex points $z_1,…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
The bidual of the closure of smooth functions with respect to the Morrey norm coincides with the Morrey space. This assertion is generalized to some Muckenhoupt weighted Morrey spaces. We combine this fact with basic extrapolation…