1,720,975 research outputs found
Embedding theorems with an exponential weight on the real semiaxis
Get PDFWe state embedding theorems between spaces of functions defined on the real semi-axis, which can grow exponentially both at 0 and at +∞
A Lagrange-type projector on the real line
Get PDFWe introduce an interpolation process based on some of the zeros of the mth generalized Freud polynomial. Convergence results and error estimates are given. In particular we show that, in some important function spaces, the interpolating polynomial behaves like the best approximation. Moreover the stability and the convergence of some quadrature rules are proved
Polynomial approximation with an exponential weight in [-1,1] (revisiting some of Lubinsky's result)
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Lagrange interpolation with exponential weights on (-1,1)
Get PDFIn order to approximate functions defined on (−1, 1) with exponential growth for |x| → 1, we consider
interpolation processes based on the zeros of orthonormal polynomials with respect to exponential weights.
Convergence results and error estimates in weighted L^p metric and uniform metric are given. In particular,
in some function spaces, the related interpolating polynomials behave essentially like the polynomial of
best approximation
Gaussian quadrature rules with an exponential weight on the real semiaxis
No full textWe consider some 'truncated' Gaussian rules based on the zeros of the orthonormal polynomials w.r.t. The weight function with x ∈ (0, +∞), α >0 and β>1. We show that these formulas are stable and converge with the order of the best polynomial approximation in suitable function spaces. Moreover, we apply these results to the related Lagrange interpolation process in weighted L 2 spaces. Finally, some numerical tests are shown
Polynomial Inequalities with an Exponential Weight on (0,+∞)
Get PDFWe consider the weight u(x) = x^γ e^(−x^(−α)−x^β) with x∈(0,+∞),
α > 0, β > 1 and γ ≥ 0, and prove Remez-, Bernstein–Markoff-, Schur and
Nikolskii-type inequalities for algebraic polynomials with the weight
u on (0,+∞)
Uniform and Convergence of the Hermite Interpolation at Pollaczek–Laguerre Zeros
Get PDFThe paper deals with the weighted polynomial approximation of functions defined on (0,+∞), which can grow exponentially both at +∞ and at 0. To this aim, we introduce interpolating operators of Hermite and Hermite–Fejér-type, based at the zeros of Pollaczek–Laguerre type orthogonal polynomials. We prove that these processes converge in weighted uniform and Lp-norms and provide sharp error estimates showing that the order of convergence is the same as the best polynomial approximation, under suitable assumptions
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