Dirichlet series and Fourier series can both be used to encode sequences of complex numbers an , n ∈ N. Dirichlet series do so in a manner adapted to the multiplicative structure of N, whereas Fourier series reflect the additive structure of N. Formally at least, the Mellin transform relates these two ways of representing sequences. In this paper, we make sense of the Mellin transform of period...

This paper introduces variations on the template matching theme that extend its usefulness by providing invariance to mean intensity-level variations, certain geometric transformations and partial obscura-tions of the target object in the image. First order statistics of the pixel by pixel diierences between the template and the image are used as a match measure in order to provide invariance t...

The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the RiemannLebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CF...

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy proc...

We study the non-parametric estimation of an unknown density f with support on R+ based i.i.d. sample multiplicative measurement errors. The proposed fully-data driven procedure is Mellin transform f, a regularisation inverse by spectral cut-off and data-driven model selection in order to deal upcoming bias-variance trade-off. introduce discuss further Mellin-Sobolev spaces which characterize r...

The commonly applied methods for seismic inversion are based on some drastic assumptions regarding the known background or macro-velocity model and the data acquisition, that limit their applicability in geologies of realistic complexity or to realistic, noisy and incomplete, data sets. The background is usually assumed smooth, often to such a degree that the wav e field can be described by sim...

Space-variant sensing is the architectural basis of all higher vertebrate visual systems (Schwartz, 1994). One evident motivation for this is that the spacecomplexity of the human visual system is reduced by up to four orders of magnitude (Rojer and Schwartz, 1990) via the use of space-variant architecture (jar a given ratio of field width to maximum resolution). This observation has obvious pr...