Results 51 to 60 of about 714 (196)

Data Driven Reconstruction Using Frames and Riesz Bases [PDF]

, 2021
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and applied in frames theory, as a data driven reconstruction procedure in inverse problems, generalizing the algorithm ...
Andrea Aspri, Leon Frischauf, Yury Korolev, Otmar Scherzer   +3 more
openaire   +3 more sources

Some relationship between G-frames and frames [PDF]

Sahand Communications in Mathematical Analysis, 2015
In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh,M. A.
Mehdi Rashidi-Kouchi, Akbar Nazari
doaj  

Pseudo-Duals of Frames and Modular Riesz Bases in Hilbert $C^\ast$-Modules [PDF]

Sahand Communications in Mathematical Analysis
In the present article, duals, approximate duals and pseudo-duals (generated by bounded and not necessarily adjointable operators) of a frame in a Hilbert $C^\ast$-module are characterized and some of their properties are obtained.
Morteza Mirzaee Azandaryani
doaj   +1 more source

Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson, Janne Nurminen, Mikko Salo   +2 more
wiley   +1 more source

Shape Derivatives of the Eigenvalues of the de Rham Complex for Lipschitz Deformations and Variable Coefficients: Part II

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 14244-14265, August 2026.
ABSTRACT In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our primary focus is on spectral perturbation problems and the differentiability of eigenvalues with respect to perturbations of the involved parameters. As a byproduct,
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron   +2 more
wiley   +1 more source

Linear Toroidal‐Inertial Waves on A Differentially Rotating Sphere with Application to Helioseismology: Modeling, Forward and Inverse Problems

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 14122-14148, August 2026.
ABSTRACT This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth‐order scalar equation.
Tram Thi Ngoc Nguyen, Damien Fournier, Laurent Gizon, Thorsten Hohage   +3 more
wiley   +1 more source

PERTURBATION OF WAVELET FRAMES AND RIESZ BASES I [PDF]

Communications of the Korean Mathematical Society, 2004
Summary: Suppose that \(\psi\in L^2(\mathbb{R})\) generates a wavelet frame (resp. Riesz basis) with bounds \(A\) and \(B\). If \(\phi\in L^2(\mathbb{R})\) satisfies \(|\widehat{\psi}(\xi)- \widehat{\phi}(\xi)| < \lambda \frac{|\xi|^\alpha } { ( 1 + | \xi | )^\gamma} \) for some positive constants \(\alpha , \gamma , \lambda\) such that \(1< 1+\alpha <
Lee, Jin, Ha, Young-Hwa
openaire   +2 more sources

Rotation invariant, Riesz bases of directional wavelets [PDF]

, 2017
International audienceThis article addresses the issue of designing bases for L 2 (R 2) that are generated by translations, rotations and dilations of a single mother wavelet ψ.
Durand, Sylvain
core   +1 more source

Decompositions of g-Frames and Duals and Pseudoduals of g-Frames in Hilbert Spaces

Journal of Function Spaces, 2015
Firstly, we study the representation of g-frames in terms of linear combinations of simpler ones such as g-orthonormal bases, g-Riesz bases, and normalized tight g-frames.
Xunxiang Guo
doaj   +1 more source