In representations using frames, oblique duality appears in situations where the analysis and synthesis has to be done different subspaces. some cases, we cannot obtain an explicit expression for duals others there exists only one dual frame which not properties need. Also, practice computations are exact. To give a solution these problems, this work introduce investigate notion of approximate ...

In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this paper we present a recent approach which determines the approximant from shift invariant subspaces by minimizing an `1-regularized least squares problem whic...

In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of L(R), 1 ≤ p ≤ ∞, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity. The space of p-integrable non-uniform splines and the shift-invariant spaces generated by finitely many localized functions are our model examples of such reproducing ker...

Computing the similarity between objects is a central task for many applications in the field of information retrieval and data mining. For finding k-nearest neighbors, typically a ranking is computed based on a predetermined set of data dimensions and a distance function, constant over all possible queries. However, many high-dimensional feature spaces contain a large number of dimensions, man...

Text Categorization(TC) is an important component in many information organization and information management tasks. Two key issues in TC are feature coding and classifier design. In this paper Text Categorization via Support Vector Machines(SVMs) approach based on Latent Semantic Indexing(LSI) is described. Latent Semantic Indexing[1][2] is a method for selecting informative subspaces of featu...

In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of L(R), 1 ≤ p ≤ ∞, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity. The space of p-integrable non-uniform splines and the shift-invariant spaces generated by finitely many localized functions are our model examples of such reproducing ker...

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...

Let X be a hypergroup. In this paper, we study the homomorphisms on certain subspaces of L(X)* which are weak*-weak* continuous.

We characterize the normal operators A on $$\ell ^2$$ and elements $$a^i \in \ell , with $$1\le i\le m$$ such that sequence $$\begin{aligned} \{ A^n a^1, \ldots a^m \}_{n\ge 0} \end{aligned}$$ is a frame. The characterization makes strong use of pseudo-hyperbolic metric $$ {{\mathbb {D}}} given in terms backward shift invariant subspaces $$H^2( )$$ associated to finite products interpolating Bl...