In a rather general setting of Itô-Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transfo...

background and aims. polymerization efficacy affects the properties and performance of composite resin restorations. the purpose of this study was to evaluate the effectiveness of polymerization of two micro-hybrid, two nano-hybrid and one nano-filled ormocer-based composite resins, cured by two different light-curing systems, using fourier transformation infrared (ft-ir) spectroscopy and vicke...

Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast (NUFFT) an alternative approach that has been mostly overlooked. With aid of experiments on a high-resolution interferometer with variety optical sources, these two methods are compared. It found NUFFT comparable in spectral profile sha...

We give a detailed study of the discrete Fourier transform (DFT) of r-even arithmetic functions, which form a subspace of the space of r-periodic arithmetic functions. We consider the DFT of sequences of r-even functions, their mean values and Dirichlet series. Our results generalize properties of the Ramanujan sum. We show that some known properties of r-even functions and of the Ramanujan sum...

In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in multidimensional Fourier transform (MDFT), which in turn provide multidimensional spatial and space-time series analysis. The complex exponential representation of sinusoid...