The aim of this paper is to study the Wold-type decomposition in class $m$-isometries. One our main results establishes an equivalent condition for analytic $m$-isometry admit $m\ge2$. In particular, we introduce $k$-kernel which use characterize $m$-isometric operators are unitarily unilateral operator valued weighted shifts As a result, also show that composition on directed graphs with one c...

A novel approach for coding textured images is presented. The texture field is assumed to be a realization of a regular homogeneous random field, which can have a mixed spectral distribution. On the basis of a two-dimensional (2-D) Wold-like decomposition, the field is represented as a sum of a purely indeterministic, harmonic, and countable number of evanescent fields. We present an algorithm ...

We call temporal aggregation the situation in which a variable that evolves through time can not be observed at all dates. This phenomenon arises frequently in economics, where it is very expensive to collect data on certain variables, and there is no reason to believe that economic time series are collected at the frequency required to fully capture the movements of the economy. For example, w...

One of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems. In applications such as database retrieval, it is important that image features used in pattern comparison provide good measures of image perceptual similarities. In this paper, we present an image model with a new set of features that address the challenge of perceptual si...

The basic problem in prediction theory is to estimate a certain, desired, behavior of the phenomenon under study (in our case a stationary process) using the information already obtained about it. In order to accomplish this we should separate completely the deterministic part from the part corrupted by noises. This is done via a Wold-type decomposition. In the case of a two-time parameter stat...

Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C∗correspondences over N 0 , generalising the classical result for a doubly commuting pair of isometries due to M. S lociński. Certain decompositions are also obtained for the general, not necessarily doubly commuting, case and several corollaries and examples are pr...

One of the fundamental challenges in pattern recognition is choosing a set of features appropriate to a class of problems. In applications such as image retrieval, it is important that features used by the system in pattern comparison provide good measures of \perceptual similarity." We present here a new set of features and an image model based on the three mutually orthogonal components produ...