We prove three results on wavelets for the Hardy space H (R). All wavelets constructed so far for H(R) are MSF wavelets. We construct a family of H-wavelets which are not MSF. An equivalence relation on H-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H-wavelets with Fourier transform discontinuous at the origin.

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are preferable. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang [2]. A cha...

we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provi...

we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provided.

We introduce ternary wavelets, based on an interpolating 4-point C ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). H...

we consider an approximation scheme using haar wavelets for solving a class of infinite horizon optimal control problems (ocp's) of nonlinear interconnected large-scale dynamic systems. a computational method based on haar wavelets in the time-domain is proposed for solving the optimal control problem. haar wavelets integral operational matrix and direct collocation method are utilized to ...

In this work, wavelets are used in the analysis of medical images, where efficiency mathematics field has been proven because basis proposed work is newly constructed mathematical equations, and through MATLAB program, many programs have designed to be ready for use image study. Physical samples were selected that compressed using wavelets, good results obtained prove method used.

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...