Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms become more challenging. A method is proposed for performing exact hypercube convolution in sub-quadratic time. The method outperforms FFTPACK, called via numpy, and FFTW, called via pyfftw...

An initial value problem for a Fractional Differential Equation (FDE) can be reformulated as a Volterra integral equation of the second kind with weakly singular kernel. Its solution can be approximated by applying suitable convolution quadratures. Methods of this type currently available in the literature are, for example, Adams product quadrature rules or Fractional Linear Multistep Methods, ...

Let μ be a compactly supported probability measure on R with expectation 1 and variance V. Let μn denote the n-time free multiplicative convolution of measure μ with itself. Then, for large n the length of the support of μn is asymptotically equivalent to eV n, where e is the base of natural logarithms, e = 2.71 . . . 1 Preliminaries and the main result First, let us recall the definition of th...

In a previous paper ([B-G1]), we defined the rectangular free convolution ⊞ λ . Here, we investigate the related notion of infinite divisibility, which happens to be closely related the classical infinite divisibility: there exists a bijection between the set of classical symmetric infinitely divisible distributions and the set of ⊞ λ -infinitely divisible distributions, which preserves limit t...

In this paper we propose three robust and semi-blind digital color image watermarking algorithms. These algorithms are based on hybrid transforms using the combination of Discrete Cosine Transform (DCT) and Singular Value Decomposition (SVD), Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD), Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT) and Singular Va...

We study convolution algebras associated with Heckman–Opdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive produ...