Showing papers by "Manos Papadakis published in 2003"
TL;DR: In this paper, a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions is presented, which can be carried out in any number of dimensions and for a big variety of dilation matrices.
Abstract: In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.
23 citations
13 Nov 2003
TL;DR: In this article, a non-separable multiresolution structure based on frames is presented, which is defined by radial scaling functions of the form of the Shannon scaling function, and can be carried out in any number of dimensions and for a great variety of dilation matrices.
Abstract: In this paper we present a non-separable multiresolution structure based on frames which is defined by radial scaling functions of the form of the Shannon scaling function. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a great variety of dilation matrices.
12 citations
TL;DR: In this paper, the authors consider additional aspects of the recently derived "minimum uncertainty" wavelets and show that they are fundamentally related to both the harmonic oscillator eigenstates and the canonical coherent states that play a fundamental role in quantum dynamics.
Abstract: We consider additional aspects of the recently derived “minimum uncertainty” (μ) wavelets. In particular, we show that they are fundamentally related to both the harmonic oscillator eigenstates and the canonical coherent states that play a fundamental role in quantum dynamics. In addition, we derive new raising and lowering operators that apply to the μ-wavelets. Finally, we explore in some detail the senses in which the μ-wavelets form complete sets that can be used in a variety of applications in quantum dynamics.
12 citations
TL;DR: In this paper, the smoothness of symmetric orthonormal wavelets arising from Hermite Distributed Approximating Functionals (HDAFs) was studied and their corresponding associated low pass filters are symmetric with respect to the origin.
2 citations