Related papers: On regular families of cardinal interpolators and …
Limiting real interpolation method is applied to describe the behaviour of the Fourier coefficients of functions that belong to spaces which are "very close" to L2.
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…
In this paper we analyze the geometric structure and properties of a certain class of subsets of $\Bbb R^d$, known in the literature as 1-multicones, and here simply called multicones, which are quite natural generalizations of the…
In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators…
We use sequences which depend on two parameters to define families of ultradifferentiable functions which contain Gevrey classes. It is shown that such families are closed under superposition, and therefore inverse closed as well.…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling…
We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.
This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity of families of such mappings in a given domain. We establish…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.
We describe several families of permutation polynomials obtained using functions with linear translators.
We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform…
A decoration of the Mandelbrot set $M$ is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials…
Nonlinear interferometers allow for mid-infrared spectroscopy with near-infrared detection using correlated photons. Previous implementations have demonstrated a spectral resolution limited by spectrally selective detection. In our work, we…
We identify a one-parameter family of inequalities for the Fourier transform whose limiting case is the restriction conjecture for the sphere. Using Stein's method of complex interpolation we prove the conjectured inequalities when the…