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Open AccessHow to compute multivariate Bessel expansions
We develop a constructive method for computing explicitly multivariate Bessel expansions of the type $$\begin{aligned} \sum _{m\ge 1} \alpha _...
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Superattracting Extraneous Fixed Points and n-cycles for Chebyshev’s Method on Cubic Polynomials
In this work we provide analytic and graphic arguments to explain the behaviour of Chebyshev’s method applied to cubic polynomials in the complex plane. In particular, we study the parameter plane related to t...
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Article
Bernoulli–Dunkl and Euler–Dunkl polynomials and their generalizations
Bernoulli–Dunkl and Euler–Dunkl polynomials are generalizations of the classical Bernoulli and Euler polynomials, using the Dunkl operator instead of the differential operator. In this paper, we study properti...
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Article
Singular Measures and Convolution Operators
We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we pr...
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Article
Heat and Poisson Semigroups for Fourier-Neumann Expansions
Given \(\alpha > -1,\) consider the second order differential operator in
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Rational values of the arccosine function
We give a short proof to characterize the cases when arccos(√r), the arccosine of the squareroot of a rational number r ∈ [0, 1], is a rational multiple of π: This happens exactly if r is an integer multiple of 1...
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Graphic and numerical comparison between iterative methods
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Fourier series of functions whose Hankel transform is supported on [0, 1]
LetJ μ denote the Bessel function of order μ. For α>−1, the system x−α/2−1/2Jα+2n+1(x1/2, n=0, 1, 2,..., is orthogonal onL 2((0, ∞),x α dx). In this paper we study the mean con...
