We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the qu...

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.

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

The rise of frame theory in appled mathematics is due to the flexibility and redundancy of frames. Structured frames are much easier to construct than Structured orthonormal bases. In this work, the notion of the ternary generalized multiresolution structure (TGMS) of subspace 2 3 ( ) L R is proposed, which is the generalization of the ternary frame multiresolution analysis. The biorthogonality...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

This paper is concerned with nonlinear inverse problems where data and solution are vector valued and, moreover, where the solution is assumed to have a sparse expansion with respect to a preassigned frame. We especially focus on such problems where the different components of the solution exhibit a common or so–called joint sparsity pattern. Joint sparsity means here that the measure (typicall...

This chapter addresses an improved approach to video face recognition (VFR). Techniques to recognize faces in video streams have been described in the literature for more than 20 years (Wang et al., 2009). Early methods were based on the still-to-still techniques which aimed at selecting good frame and did some relative processing. Recently researchers began to truly solve such problems by spat...

In this contribution, we extend the reassignment method (RM) and synchrosqueezing transform (SST) to arbitrary time-frequency localized lters and, in the rst case, arbitrary downsampling factors. A su cient condition for the invertibility of the SST is provided. RM and SST are techniques for deconvolution of shorttime Fourier and wavelet representations. In both methods, the partial phase deriv...

It is well known, the voice segments and coincident data packets are not equally valued and significant for decoding and comprehension of speech signal. Some lost segments may only slightly worsen audible quality, while others cause strong distortion of the speech signals. Despite this, the feature of different importance of different voice segments in current generation of digital voice transm...

We present synchronized recursive timed automata (SRTA) that extend timed automata with a stack. Each frame of a stack is composed of rational-valued clocks, and SRTA synchronously increase the values of all the clocks within the stack. Our main contribution is to show that the reachability problem of SRTA is ExpTime-complete. This decidability contrasts with the undecidability for recursive ti...