نتایج جستجو برای: frame operator

تعداد نتایج: 193568  

Journal: :Adv. Comput. Math. 2014
Peter G. Casazza Jesse Peterson

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unitweight fusion frames with these properties is the flexible a...

Journal: :Rocky Mountain Journal of Mathematics 2021

In the signal-processing literature, a frame is mechanism for performing analysis and reconstruction in Hilbert space. By contrast, quantum theory, positive operator-valued measure (POVM) decomposes Hilbert-space vector purpose of computing measurement probabilities. Frames their most common generalizations can be seen to give rise POVMs, but does every reasonable POVM arise from type frame? We...

Journal: :sahand communications in mathematical analysis 0
mahdiyeh khayyami department of mathematics, science and research branch, islamic azad university, kerman, iran. akbar nazari department of mathematics, science and research branch, islamic azad university, kerman, iran.

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

Journal: :CoRR 2013
Jie Fan Yanjing Wang Hans van Ditmarsch

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw(φ → ψ) → (Kwφ → Kwψ). Knowing whether logic cannot define many common frame properties, and its expressive po...

2016
Ben Adcock Daan Huybrechs

This document contains supplementary materials for the paper Frames and numerical approximation by B. Adcock & D. Huybrechs [3]. SM1 Example 1. Fourier frames for complex geometries Consider the frame (3.1) over a domain Ω ⊆ (−1, 1)d. SM1.1 The kernel of G We first characterize the kernel of the Gram operator: Proposition SM1.1. Let G be the Gram operator (2.7) of the frame (3.1). Then Ker(G) =...

2012
Fredrik Lindgren

This thesis is concerned with numerical approximation of linear stochastic partial differential equations driven by additive noise. In the first part, we develop a framework for the analysis of weak convergence and within this framework we analyze the stochastic heat equation, the stochastic wave equation, and the linearized stochastic Cahn-Hilliard, or the linearized Cahn-Hilliard-Cook equatio...

2004
Muhammad Sabieh Anwar

(a) The expectation value of a component 〈α|V̂i|α〉 remains unchanged in the rotated frame (with respect to the transformed operator), i.e., 〈α′|V̂ ′ i |α′〉 = 〈α|V̂i|α〉 where |α〉 −→ D(R)|α〉 = |α′〉 and V̂ ′ i is the operator transform. The expectation value in the two bases must be the same, because we are assuming that space is isotropic, and all physical observables and physical laws must remain in...

1997
Thomas Strohmer

| The Gabor transform yields a discrete representation of a signal in the phase space 1, 2]. Since the Gabor transform is non-orthogonal, eecient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so-called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, bas...

Journal: :EURASIP J. Adv. Sig. Proc. 2006
Yonina C. Eldar Ole W. Christensen

Given a frame for a subspace W of a Hilbert space H , we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a gener...

2002
CHARLES K. CHUI QIYU SUN David R. Larson

Let Ψ = {ψ1, . . . , ψL} ⊂ L2 := L2(−∞,∞) generate a tight affine frame with dilation factor M , where 2 ≤M ∈ Z, and sampling constant b = 1 (for the zeroth scale level). Then for 1 ≤ N ∈ Z, N×oversampling (or oversampling by N) means replacing the sampling constant 1 by 1/N . The Second Oversampling Theorem asserts that N×oversampling of the given tight affine frame generated by Ψ preserves a ...

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