Wavelets frame associated to accretive function

Tight frame wavelets and the dimension function

Wavelets with Frame Multiresolution Analysis

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...

Implicit Function Theorems for M-accretive and Locally Accretive Set-valued Mappings

In this paper we elaborate new methods to the theory of parametric generalized equations governed by accretive mappings. Two implicit function theorems will be proved, one for m-accretive and another for locally accretive and continuous set-valued mappings. Making use of the theorem for m-accretive mappings we will study parametric nonlinear evolution problems. It will be also shown that there ...

Generalization Analysis of Wavelet Frame based Neural Network for Function Representations using Compactly supported Gaussian Wavelets

A new type of Wavelet Neural Network (WNN) has been proposed to enhance the function approximation and generalization performance generating an optimal size network. In the proposed WNN, the nonlinear activation function is a linear combination of wavelets that can be updated during the network training process. As a result the approximate error is significantly decreased. The RBF network based...

Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets

Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...