Results 11 to 20 of about 50,797 (262)
$G$-Frames Generated by Iterated Operators [PDF]
Sahand Communications in Mathematical Analysis, 2023 Assuming that $\Lambda$ is a bounded operator on a Hilbert space $H$, this study investigate the structure of the $g$-frames generated by iterations of $\Lambda$.
Morteza Rahmani
doaj +3 more sources
Richardson and Chebyshev Iterative Methods by Using G-frames [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $.
Hassan Jamali, Mohsen Kolahdouz
doaj +9 more sources
Scalability of Frames Generated by Dynamical Operators [PDF]
Frontiers in Applied Mathematics and Statistics, 2017 Let ℍ be a separable Hilbert space, let G ⊂ ℍ, and let A be an operator on ℍ. Under appropriate conditions on A and G, it is known that the set of iterations FG(A)={Ajg|g∈G,0≤j≤L(g)} is a frame for ℍ.
Roza Aceska, Yeon H. Kim
doaj +3 more sources
Computer Graphics Forum, 2021 AbstractDifferential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second‐order operators, as well as higher‐order operators such as the Bilaplacian, have been discretized for ...
D. Palmer, O. Stein, J. Solomon
openaire +4 more sources
Frames and weak frames for unbounded operators [PDF]
Advances in Computational Mathematics, 2020 In 2012 Găvruţa introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this article we revisit these concepts for an unbounded and densely defined operator $A:\mathcal{D}(A)\to\mathcal{H}$ in two ...
Giorgia Bellomonte, Rosario Corso
openaire +3 more sources
Lower Semi-frames, Frames, and Metric Operators [PDF]
Mediterranean Journal of Mathematics, 2020 AbstractThis paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated with the function be dense.
J.-P. Antoine, R. Corso, C. Trapani
openaire +2 more sources
Frame-related operators for woven frames [PDF]
International Journal of Wavelets, Multiresolution and Information Processing, 2019 A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et al. In the study of frames, some operators like analysis, synthesis, Gram and frame operators play the central role. In this paper, for the first time, we introduce and define these operators for woven-weaving frames and review some of their ...
Asghar Rahimi +2 more
openaire +3 more sources
Transactions of the American Mathematical Society, 2009 We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity (e.g., multiframes) their dilation approach.
Kaftal, Victor +2 more
openaire +2 more sources
Frame soft shrinkage operators are proximity operators [PDF]
Applied and Computational Harmonic Analysis, 2022 In this paper, we show that the commonly used frame soft shrinkage operator, that maps a given vector ${\mathbf x} \in {\mathbb R}^{N}$ onto the vector ${\mathbf T}^{\dagger} S_γ {\mathbf T} {\mathbf x}$, is already a proximity operator, which can therefore be directly used in corresponding splitting algorithms.
Geppert, Jakob Alexander +1 more
openaire +3 more sources
Generalized atomic subspaces for operators in Hilbert spaces [PDF]
Mathematica Bohemica, 2022 We introduce the notion of a $g$-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of $g$-fusion frames.
Prasenjit Ghosh, Tapas Kumar Samanta
doaj +1 more source