Related papers: A Construction of Biorthogonal Wavelets With a Com…
We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the…
We introduce a compact operator-based technique that solves the paraxial wave equation for a broad class of structured light fields. Using the spatial evolution operator to propagate two families of physically apodized inputs, Gaussian…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
The mechanism of wavefront reconstruction by a geometric-optical reflection of reconstructing light from surfaces with constant phase differences between the object and reference waves used to record the interference fringe structure in the…
In this paper, we provide some sufficient conditions for the compactness of weighted composition operators on Dirichlet space. Furthermore, we characterize the numerical range of certain classes of weighted composition operators on…
In the framework of one dimensional potential scattering we prove that, modulo a compact term, the wave operators can be written in terms of a universal operator and of the scattering operator. The universal operator is related to the one…
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in…
We present a geometrical demonstration for persistence properties for a bi-Hamiltonian system modelling waves in a shallow water regime. Both periodic and non-periodic cases are considered and a key ingredient in our approach is one of the…
We characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces
We establish compactness estimates for $\bar{\partial}_{M}$ on a compact pseudoconvex CR-submanifold $M$ of $\mathbb{C}^{n}$ of hypersurface type that satisfies the (analogue of the) geometric sufficient conditions for compactness of the…
Objective. Dual-energy computed tomography (DECT) has the potential to improve contrast, reduce artifacts and the ability to perform material decomposition in advanced imaging applications. The increased number or measurements results with…
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order…
We give a geometric characterization of the elements of a TRO that can be represented as compact operators by a faithful representation of the TRO.
Compact binary systems with total masses between tens and hundreds of solar masses will produce gravitational waves during their merger phase that are detectable by second-generation ground-based gravitational-wave detectors. In order to…
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the…
This paper presents an efficient implementation of the Wavenet generation process called Fast Wavenet. Compared to a naive implementation that has complexity O(2^L) (L denotes the number of layers in the network), our proposed approach…
In the paper we design a Parseval wavelet frame with a compact support. The corresponding refinement mask uniformly approximates an arbitrary continuous periodic function $f$, $f(0)=1$, $|f(x)|^2+|f(x+\pi)|^2\le 1$. The refinable function…
Correlative computational microscopy can accelerate imaging and modeling of cellular dynamics by relaxing trade-offs inherent to dynamic imaging. Existing computational microscopy frameworks are either specialized or overly generic,…
This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…