We analyze the convergence and smoothness of certain class of nonlinear subdivision schemes. We study the stability properties of these schemes and apply this analysis to the speci c class based on ENO and weighted-ENO interpolation techniques. Our interest in these techniques is motivated by their application to signal and image processing.

Abstract. Refinable functions and cascade algorithms play a fundamental role in wavelet analysis, which is useful in many applications. In this paper we shall study several properties of refinable functions, cascade algorithms and wavelets, associated with Hölder continuous masks, in the weighted subspaces L2,p,γ(R) of L2(R), where 1 � p � ∞, γ � 0 and f ∈ L2,p,γ(R) means

Wavelet transforms have been one of the important signal processing developments in the last decade, especially for applications such as time-frequency analysis, data compression, segmentation and vision. Although several efficient implementations of wavelet transforms have been derived, their computational burden is still considerable. This paper describes two generic parallel implementations of wavelet transforms based on the pipeline processor farming methodology which have the potential to achieve real-time performance. Results show that the parallel implementation of the over-sampled Wavelet Transform achieves virtually linear speedup, while the parallel implementation of the Discrete Wavelet Transform (DWT) also out-performs the sequential version, provided that the filter order is large. The DWT parallelisation performance improves with increasing data length and filter order while the frequency domain implementation performance is independent of wavelet filter order. Parallel p...

This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically the cascade algorithm in wavelet theory. Let H be a Hilbert space, and let π be a representation of L ∞ (T) on H. Let R be a positive operator in L ∞ (T) such that R (11) = 11, where 11 denotes the constant function 1. We study operators M on H (bounded, but noncontractive) such that π (f) M = Mπ ( f ( z 2)) and M ∗ π (f)M = π (R ∗ f), f ∈ L ∞ (T), where the ∗ refers to Hilbert space adjoint. We give a complete orthogonal expansion of H which reduces π such that M acts as a shift on one part, and the residual part is H (∞) = ⋂ n [MnH], where [MnH] is the closure of the range of Mn. The shift part is present, we show, if and only if ker (M ∗ ) ̸ = {0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation π, we show that, for this wavelet

Abstract. In this paper, we obtain symmetric C ∞ real-valued tight wavelet frames in L2(R) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported C ∞ orthonormal complex wavelets in L2(R). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in L2(R) is given. 1.

Abstract. This paper deals with generalized coiflets designed in [Monzón, Beylkin, Hereman, 1999] and with computing their scaling coefficients, respectively. Such wavelets are useful in applications where interpolation and linear phase are of importance. We derive alternative definitions and prove their equivalence. In all definitions the system with minimal number of equations is proposed, the third definition enables to eliminate some quadratic conditions occurring in original definition. Moreover, by their construction, one additional free parameter is obtained and we propose how to choose this parameter to further simplify the arising system. Similar approach was also used in [ Černá, Finěk, 2004c]. For small filter lengths this system can be explicitly solved with algebraic methods like Gröbner bases. The simple structure of arising polynomials (in one variable) allows to find quickly all possible solutions. In addition to the examples of coiflets of length 18 presented in [Monzón, Beylkin, Hereman, 1999] we have found another ‘maximal coiflets’.

Web service development and usage has shifted from simple information processing services to high-value business services that are crucial to productivity and success. In order to deal with an increasing risk of unavailability or failure of mission-critical Web services we argue the need for advanced reservation of services in the form of derivatives. The contribution of this paper is twofold: First we provide an abstract model of a market design that enables the trade of derivatives for mission-critical Web services. Our model satisfies requirements that result from service characteristics such as intangibility and the impossibility to inventor services in order to meet fluctuating demand. It comprehends principles from models of incomplete markets such as the absence of a tradeable underlying and consistent arbitragefree derivative pricing. Furthermore we provide an architecture for a Web service market that implements our model and describes the strategy space and interaction of market participants in the trading process of service derivatives. We compare the underlying pricing processes to existing derivative models in energy exchanges, discuss eventual shortcomings, and propose Wavelets as a preprocessing tool to analyze actual data and extract long- and short-term seasonalities.

In this paper, we establish formulas for the configuration of a special class of irreducible representations of the Cuntz algebra ON, N = 2, 3,...,∞. These irreducible representations arise as subrepresentations of naturally occurring representations of O_N acting in L2 (T) and arise from consideration of multiresolution wavelet filters.