This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist { a j / 2 ? ( ? ? k b ) } , ? Z in L R for which no frame has structure. We first generalize this result by proving approximately Motivated we show imposing very mild decay condition on the Fourier transform of generator certain oversampling N indeed an frame; most importantly, ...

The main purpose of this paper is to find other measurements for constructing optimal duals that minimize the reconstruction errors, when erasures occur. Some known results are investigated with some measurements. Moreover, we investigate extreme points set all 1-erasure by seminorms. Furthermore, examples provided clarification.

Article history: Received 7 June 2011 Revised 7 December 2011 Accepted 30 December 2011 Available online 3 January 2012 Communicated by Karlheinz Gröchenig

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.

In this paper, we introduced and characterized the controlled $g$-duals of a frame in separable Hilbert space $\mathcal{H}$ . Afterwards, obtained new $C$-controlled $g$-dual frames from given frames. addition, approximation for was defined some their properties were investigated. Finally, relationship between approximately dual $g$-dual.

The berization of a ne systems via dual Gramian techniques, that was developed in previous papers of the authors, is applied here for the study of a ne frames which have an a ne dual system. Gramian techniques are also used to verify whether a dual pair of a ne frames is a also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of a ne frames from an ...