Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, such as, distributed processing, wireless sensor networks, packet encoding. Inspired by the work of Bemrose et al.[12], this paper delves into the properties and characterizations of weaving fusion frames.

Two frames fn∞n=1 and gn∞n=1 in a separable Hilbert space H are said to be weaving frames, if for every s σ N, fnnσ Ugnneσ is a frame for H. Weaving frames are proved to be very useful in many areas, such as, distributed processing, wireless sensor networks, packet encoding and many more. Inspired by the work of Bemrose et al.[11], this paper delves into the properties and characterizations of weaving frames and weaving Riesz bases.

In this paper we study various properties and characterizations of weaving frames in Krein spaces. In support of our findings, several examples and counter examples are provided, illustrating the applicability of the theoretical results. Additionally, we extend the discussion to an important application in probabilistic erasure, highlighting how weaving frames can be used to mitigate data loss in such scenarios.

Multiresolution analysis is a mathematical tool used to decompose functions in different resolution subspaces, where the scaling function plays a key role to construct the nested subspaces in L2(R) . This paper presents a generalization of the same in L2(Qp) , called frame multiresolution analysis (FMRA). So FMRA is a generalization of multiresolution analysis with frame condition. We study various properties of FMRA including characterizations in L2(Qp) . Furthermore, frame scaling sets are studied with examples.

Abstract: Frames play significant role as redundant building blocks in distributed signal processing. Getting inspirations from this concept, Bemrose et al. produced the notion of weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. This article presents a flavor of weaving multiframelets. Various properties of weaving multiframelets are explored in the p -adic number field. Furthermore, several characterizations of p -adic weaving multiframelets have been analyzed.

In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-frame and fusion frame. K-fusion frames come naturally, having significant applications, when one needs to reconstruct functions (signals) from a large data in the range of a bounded linear operator. Motivated by the concept of weaving frames, in this paper we study wovenness of K-fusion frames. This article presents characterizations of weaving K-fusion frames. Paley-Wiener type perturbations and conditions on erasure of frame components are discussed to examine wovenness.

Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, for example, wireless sensor networks. In this paper, we discuss a generalization of fusion frames, K-fusion frames. K-fusion frames provide decompositions of a Hilbert space into atomic subspaces with respect to a bounded linear operator. This article studies various kinds of properties of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.

This article presents a discussion on p-adic multiframe by means of its wavelet structure, called as multiframelet, which is build upon p-adic wavelet construction. Various properties of multiframelet sequence in L2(Qp) have been analyzed. Furthermore, multiframelet in Qp has been engendered and scrutinized through several properties of associated multiframelet operator, erasure and Paley-Wiener type perturbation of corresponding multiframelet components.

This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the notion of K-fusion frames. Characterizations of K-fusion frames are discussed. Various properties of K-fusion frames, for example, direct sum, intersection, are studied.

In a separable Hilbert space L(H,K), two frames {fi}i I and {gi}i I are said to be woven if there are constants 0 < A ≤ B so that for every σ I, {fi}i σ {gi}i σc forms a frame for L(H,K) with the universal bounds A,B. This paper provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.

In distributed signal processing frames play significant role as redundant building blocks. Bemrose et al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. This article focuses on study, characterization of weaving K-frames in different spaces. Paley-Wiener type perturbations and conditions on erasure of frame components have been assembled to scrutinize woven-ness of K-frames.