In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on IR d. More precisely, we characterize the functions in the Schwartz space S(IR d) and in L 2 k (IR d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support. 1 Introduction In the last few years there has been a great interest to real Paley-Wiener theorems for certain integral transforms, see [...

We extend the recent sparse Fourier transform algorithm of [1] to the noisy setting, in which a signal of bandwidth N is given as a superposition of k N frequencies and additive noise. We present two such extensions, the second of which exhibits a novel form of error-correction in its frequency estimation not unlike that of the β-encoders in analog-to-digital conversion [2]. The algorithm runs ...

In this paper, we study the transient behavior of a level dependent PH/PH/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the overflow losses that are due to a full queue and the los...

In this study, we explore the domain of orthogonal transforms, in order to bring an understanding on the characterization of image features, with emphasis placed on the Karhunen-Loeve (K-L) transform for its optimal energy packing properties. The study's wnmbution is in establishing a thorough research base that relates the eigensystem and transform domain properties of the K-L transform to two...

We present a new method to investigate a class of diagrams which generalizes the sunset topology to any number of massive internal lines. Our attention is focused on the computation of the spectral density of these diagrams which is related to manybody phase space in D dimensional space-time. The spectral density is determined by the inverse K-transform of the product of propagators in configur...

1 Review 1.1 Setup In the previous lecture, we considered an apparatus consisting of three planes: • an aperture plane. Coordinates on the aperture plane are denoted by x and y. • a transform plane. Coordinates on the transform plane are denoted by X and Y. • an image plane. Coordinates on the image plane are denoted by x and y. We defined the spatial frequencies, µ = k f X ν = k f Y where f is...

In this research project, the nitrito nitro isomerization of [Co (NH3)5No2]F2 complex has been studied. Isomerization of this complex in the solid state follows a first order kinetics. The rate of isomerization at different temperatures was determined using a Fourier Transform Lnfrared Spectrophotometer. ? and ? are calculated at 298 K. The infrared, visible and ultraviolet spectra of th...