A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...

To overcome the limitation induced by the fixed timefrequency resolution over the whole time-frequency plane of Gabor frames, we propose a simple extension of the Gabor theory leading to the construction of frames with timefrequency resolution evolving over time or frequency. We describe the construction of such frames and give the explicit formulation of the canonical dual frame for some condi...

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

Abstract We show spectral invariance for faithful $$*$$ ? -representations a class of twisted convolution algebras. More precisely, if G is locally compact group with continuous 2-cocycle c which the corresponding Mackey $$G_c$$ G c</mml:...

Introduction Today, surveyors in both the private and public sectors are facing considerable challenges with random digit dialed (RDD) landline telephone samples. The population coverage rates for landline telephone surveys are being eroded by wireless-only households, portable telephone numbers, telecommunication barriers (e.g., call forwarding, call blocking and pager connections), technologi...

For a wavelet frame with polynomial symbols generated by an MRA with a given approximation order, we present the method for parametric description and construction of all dual analysis operators (filter banks) with the maximum number of vanishing moments whose symbols are polynomials. The similar problems related to the maximum frame approximation order and some other wavelet frame properties a...

A Gabor or Weyl-Heisenberg frame for L2(Rd) is generated by time-frequency shifts of a square-integrable function, the Gabor atom, along a time-frequency lattice. The dual frame is again a Gabor frame, generated by the dual atom. In general, Gabor frames are not stable under a perturbation of the lattice constants; that is, even for arbitrarily small changes of the parameters the frame property...

We use a generalization of Wiener’s 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L∞, ` )(R), the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs also to W (L∞, ` )(R).

BACKGROUND, AIMS AND DESIGN The increase in mobile telephone-only households may be a source of bias for traditional landline gambling prevalence surveys. Aims were to: (1) identify Australian gambling participation and problem gambling prevalence using a dual-frame (50% landline and 50% mobile telephone) computer-assisted telephone interviewing methodology; (2) explore the predictors of sample...