Motivated by the harmonic analysis of selfaffine measures, we introduce a class representations Cuntz algebra associated to random walks on graphs. The are constructed using dilation theory row coisometries. We study these representations, their commutant and intertwining operators.

We extend the notion of dilation distance to strongly continuous one-parameter unitary groups. If dilation distance between two such groups is finite, then these can be represented on same space in a way that their generators have domain and are fact bounded perturbation one another. This result extends <mml:math xmlns:mml="http://www...

We prove that non-self-adjoint harmonic and anharmonic oscillator operators have non-trivial pseudospectra. As a consequence, the computation of high energy resonances by the dilation analyticity technique is not numerically stable.

Edge detection plays a important role in image analysis. It is used to detect the different edges in the images. By using the combination of different morphological operators in the proposed method like erosion, dilation with the different edge operators like Robert ,prewitt, sobel, log and canny to find the edges by using the structure element. The fine edges in different direction can be dete...

Motivated by recent developments in the study of finitedimensional frames, this work develops an independent theory of finitedimensional wavelet systems on the circle. Using natural translation and dilation operators, trigonometric polynomial, orthonormal scaling functions are constructed which give rise to finite-dimensional multiresolution analyses and, consequently, orthonormal wavelet syste...

We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new ope...

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related linear operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that admit an orthonormal modular Riesz basis. Interrelations and applications t...

We study multivariate trigonometric polynomials satisfying the “sum-rule” conditions of a certain order. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest in the analysis of convergence and smoothness of multivariat...

In this text we show how points, point pairs, lines, planes, circles, spheres, and rotation, translation and dilation operators and their uncertainty can be evaluated from uncertain data in a unified manner using the Geometric Algebra of conformal space. This extends previous work by Förstner et al. [3] from points, lines and planes to non-linear entities and operators, while keeping the linear...

We give complete descriptions of the set square roots certain classical operators, often providing specific formulas. The operators included in this discussion are unilateral shift, Volterra operator, compress