Ein Beitrag zur Theorie der Orthogonalpolynome.
Einfache verallgemeinerte klassische Orthogonalpolynome.
Electrostatic Interpretation and Bounds for the Extreme Zeros of Classical Orthogonal Polynomials
Electrostatics and ghost poles in near best fixed pole rational interpolation.
Elliptic biorthogonal polynomials connected with Hermite's continued fraction.
Entropy of Hermite polynomials with application to the harmonic oscillator.
Equiconvergence and equisummability of Jacobi series
2010 Mathematics Subject Classification: 33C45, 40G05.In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi polynomials.
Errata to the paper: "Construction of the lowest-order recurrence relation for the Jacobi coefficients'' (Zastos, Mat. 17 (1983), pp. 655-675)
Estimates for polynomials in the unit disk with varying constant terms
Let || · || be the uniform norm in the unit disk. We study the quantities Mn (α) := inf (||zP(z) + α|| - α) where the infimum is taken over all polynomials P of degree n - 1 with ||P(z)|| = 1 and α > 0. In a recent paper by Fournier, Letac and Ruscheweyh (Math. Nachrichten 283 (2010), 193-199) it was shown that infα>0Mn (α) = 1/n. We find the exact values of Mn (α) and determine corresponding extremal polynomials. The method applied uses known cases of maximal ranges of polynomials.
Estimates for polynomials orthogonal with respect to some Gegenbauer-Sobolev type inner product.
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
Euler polynomials and the related quadrature rule.
Evaluation of associated Legendre functions off the cut and parabolic cylinder functions.
Evaluations of some determinants of matrices related to the Pascal triangle.
Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem.
Expansion of analytic functions in series of classical orthogonal polynomials
Exponential Riordan arrays and permutation enumeration.