相关论文: Chromatic derivatives, chromatic expansions and as…
This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential…
Chromatic derivatives and series expansions of bandlimited functions have recently been introduced in signal processing and they have been shown to be useful in practical applications. We extend the notion of chromatic derivative using…
We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the…
We are studying here the classical operator creating secondary polynomials associated with an orthogonal system for a continuous probability density function on a real interval. We know it is possible with the coupling of Stietjes…
A generic differential operator on the vectorial space of polynomial functions was presented in a recent work and applied in the study of differential relations fulfilled by polynomial sequences either orthogonal or 2-orthogonal. Using the…
Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
A family of orthonormal bases, the ultrametric wavelet bases, is introduced in quadratically integrable complex valued functions spaces for a wide family of ultrametric spaces. A general family of pseudodifferential operators, acting on…
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
We study a family of bivariate orthogonal polynomials associated to the deltoid curve. These polynomials arise when classifying bivariate diffusion operators that have discrete spectral decomposition given by orthogonal polynomials with…
Following the pioneering work of Duistermaat and Gr\"unbaum, we call a family $\{p_n(x)\}_{n=0}^{\infty}$ of polynomials bispectral, if the polynomials are simultaneously eigenfunctions of two commutative algebras of operators: one…
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them, its explicit expression, the connection with the Euler numbers, its integral representation via the Kontorovich-Lebedev…
Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic…
Certain Bernoulli convolution measures (\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…