相关论文: Unitary matrix functions, wavelet algorithms, and …

This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…

Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly…

Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…

As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…

In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…

The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…

The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear…

In this paper, we describe some recent results obtained in the context of vector subdivision schemes which possess the so-called full rank property. Such kind of schemes, in particular those which have an interpolatory nature, are connected…

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

Relation of ultrametric analysis, wavelet theory and cascade models of turbulence is discussed. We construct the explicit solutions for the nonlinear ultrametric integral equation with quadratic nonlinearity. These solutions are built by…

We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant…

Biosignals are nowadays important subjects for scientific researches from both theory and applications especially with the appearance of new pandemics threatening humanity such as the new Coronavirus. One aim in the present work is to prove…

We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the…

We describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of…

The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…

A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the…

By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…

We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…