In the first part of this paper, we consider nonlinear extension of frame theory by introducing bi-Lipschitz maps F between Banach spaces. Our linear model of bi-Lipschitz maps is the analysis operator associated with Hilbert frames, p-frames, Banach frames, g-frames and fusion frames. In general Banach space setting, stable algorithm to reconstruct a signal x from its noisy measurement F (x) +...

Motivated to generalize the Fourier frame concept Banach spaces we introduce (p, q)-Bessel/frame measures for a given finite measure on LCA groups. We also present general way of constructing measure. Moreover, prove that if has an associated q)-frame measure, then it must have certain uniformity in sense weight is distributed quite uniformly its support. Next, show μ and λ without atoms whose ...

We show that multi-window Gabor frames with windows in the Wiener algebra W (L∞, `) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra also belongs to this space. Our proofs are mostly based on recent noncommutative versions of Wiener’s 1/f lemma.

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted Lp-spa...

The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces ...

* Correspondence: poom. [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s University, of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand Full list of author information is available at the end of the article Abstract In this article, we introduce a new iterative scheme for finding a common element of the set of fixed points of strongly relatively nonexp...

The given article describes the implicit fractional dierential equation with anti-periodic boundary conditionsin frame of Caputo-Katugampola derivative. We obtain an analogous integral thegiven problem and prove existence uniqueness results such a using Banach andKrasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, Ulam-Hyersstability are discussed. To show ee...

We prove that \(L_2(\mathbb {R})\) contains a Schauder basis of non-negative functions. Similarly, for all \(1<p<\infty \), \(L_{p}(\mathbb basic sequence functions such \(L_p(\mathbb embeds into the closed span sequence. as well if X is separable Banach space with bounded approximation property, then any set in dense quasi-basis (Schauder frame) X.