We propose a matrix approach to the computation of BattleLemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m . The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m . We approximate this bi-infinite ma...

in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.

cupric oxide nanostructures were synthesized via a simple reaction between copper nitrate and sodium hydroxide using a sonochemical-assisted method. the synthesized cuo was then characterized using x-ray diffraction, scanning electron microscopy, transmission electron microscopy, fourier transform infrared, ultraviolet-visible and photoluminescence spectroscopy. our studies show that the cuo na...

In the present article, we define Mexican hat wavelet Stieltjes transform (MHWST) by applying concept of [9]. The proposed serves as a centralized method to analyze both discrete and continuous time-frequency localization. Besides formulation all fundamental results, reconstruction formula is also obtained for MHWST. Further, unified approach applied obtain necessary sufficient conditions same....

Several errors were introduced in the preparation of this article for publication. In the third sentence of the "Random walk with one turning angle" section of the Results, a symbol was removed from the definition of the Fourier-Laplace-transform. The correct definition can be found here:

In this paper we will study the existence of fundamental solutions for the explicit and implicit backward time dependent Schödinger equation, via discrete Fourier transform and its symbol for the Laplace operator. In both cases we will prove that the discrete fundamental solutions obtained converges to the continuous fundamental solution in the l1−norm sense.

We investigate the Weyl calculus of pseudodifferential operators with the methods of time-frequency analysis. As symbol classes we use the modulation spaces, which are the function spaces associated to the short-time Fourier transform and the Wigner distribution. We investigate the boundedness and Schatten-class properties of pseudodifferential operators, and furthermore we study their mapping ...

Optical communications based on Nonlinear Fourier Transform (NFT) and digital coherent transceivers are proposed as a new theoretical framework for over the nonlinear optical fiber channel. For discrete eigenvalue transmissions (or soliton transmissions), one seeks to encode much information possible in each degree of freedom shorten distance between neighboring pulses increase overall bit rate...

This dissertation reports research about the phase space perspective for solving wave problems, with particular emphasis on the phenomenon of mode conversion in multicomponent wave systems, and the mathematics which underlie the phase space perspective. Part I of this dissertation gives a review of the phase space theory of resonant mode conversion. We describe how the WKB approximation is rela...