Related papers: Interpolatory Estimates, Riesz Transforms and Wave…
A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…
Optical interferometry provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Through direct observation of rotationally distorted photospheres at sub-milliarcsecond scales, we are now able to…
The scale dependent intermittency exponents in developed hydrodynamic turbulence are calculated assuming a natural hierarchy of correlations in the turbulence. The major correlations are taken into account explicitly, while the remaining…
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or approximation of vector-valued functions on Delaunay meshes in…
We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for…
In this paper, an equivalence between existence of particular exponential Riesz bases for multivariate bandlimited functions and existence of certain polynomial interpolants for these bandlimited functions is given. For certain classes of…
The polarization state of electromagnetic radiation scattered by atmospheric particles such as aerosols, cloud droplets, or ice crystals contains much more information about the optical and microphysical properties than the total intensity…
The symplectic wavelet transformation [Opt. Lett. 31 (2006) 3432], which is related to quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable…
Algebraic convergences rates of (iterated) Tikhonov regularization for linear inverse problems in Hilbert spaces are characterized by the membership of the exact solution to intermediate spaces produced by the K-method of real…
The problem of large-scale correlations of particles produced in high-energy collisions is discussed. Among them are, e.g., those correlations which lead to ring-like and elliptic flow shapes of individual high-multiplicity events in the…
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…
Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the…
This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, $\omega(\theta_\mathbf{k})$ ($\theta_\mathbf{k}$:…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…