In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H . We further give necessary and sufficient conditions on g-Besse...

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...

L-BFGS is a hill climbing method that is guarantied to converge only for convex problems. In computer graphics, it is often used as a black box solver for a more general class of non linear problems, including problems having many local minima. Some works obtain very nice results by solving such difficult problems with L-BFGS. Surprisingly, the method is able to escape local minima: our interpr...

The orthonormal basis generated by a wavelet of L 2 (R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L 2 (R d) is called the multiwavelet packet basis. The concept of wavelet frame packet is also gen...

It is well-known that the sum of two $z$-ideals in $C(X)$ is either $C(X)$ or a $z$-ideal. The main aim of this paper is to study the sum of strongly $z$-ideals in ${mathcal{R}} L$, the ring of real-valued continuous functions on a frame $L$. For every ideal $I$ in ${mathcal{R}} L$, we introduce the biggest strongly $z$-ideal included in $I$ and the smallest strongly $z$-ideal containing ...

We characterize L norms of functions on R for 1 < p < ∞ in terms of their Gabor coefficients. Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions of L functions converge to the functions almost everywhere and in L for 1 < p < ∞. In L we prove an analogous result: the Gabor expansions converge to the functions almost everywhere and in L in a certain Cesàro sense. Consequ...

We discuss the physical equivalence between the Einstein and Jordan frames in Brans-Dicke theory. The inequivalence of conformal transformed theories is clarified with the help of an old equivalence theorem of Chrisholm’s. 04.20. Fy, 04.50. +h Typeset using REVTEX 1 Brans-Dicke theory is a natural generalization of Einstein theory. In Brans-Dicke theory, the effective gravitational constantGeff...

Frames consisting of translates of a single function play an important role in sampling theory as well as in wavelet theory and Gabor analysis. We give a necessary and sufficient condition for a subfamily of regularly spaced translates of a function φ ∈ L(R), (τnbφ)n∈Λ, Λ ⊂ Z, to form a frame (resp. Riesz basis) for its closed linear span. One consequence is that if Λ ⊂ N , then this family is ...

Let H be a separable Hilbert space, let G ⊂ H, and let A be an operator on H. Under appropriate conditions on A andG, it is known that the set of iterations FG(A) = {Ag | g ∈ G, 0 ≤ j ≤ L(g)} is a frame for H. We call FG(A) a dynamical frame for H, and explore further its properties; in particular, we show that the canonical dual frame of FG(A) also has an iterative set structure. We explore th...

We study singly-generated wavelet systems on R that are naturally associated with rank-one wavelet systems on the Heisenberg group N . We prove a necessary condition on the generator in order that any such system be a Parseval frame. Given a suitable subset I of the dual of N , we give an explicit construction for Parseval frame wavelets that are associated with I . We say that g ∈ L(I×R) is Ga...