Embedding theorems with an exponential weight on the real semiaxis

We state embedding theorems between spaces of functions defined on the real semi-axis, which can grow exponentially both at 0 and at +∞

L^p-convergence of Fourier sums with exponential weights on (-1,1)

AbstractIn order to approximate functions defined on (−1,1) and having exponential singularities at the endpoints of the interval, we study the behavior of some modified Fourier Sums in an orthonormal system related to exponential weights. We give necessary and sufficient conditions for the boundedness of the related operators in suitable weighted Lp-spaces, with 1<p<∞. Then, in these spaces, these processes converge with the order of the best polynomial approximation

Polynomial Inequalities with an Exponential Weight on (0,+∞)

We 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,+∞)

Polynomial approximation with Pollaczeck-Laguerre weights on the real semiaxis. A survey. ETNA - Electronic Transactions on Numerical Analysis

This paper summarizes recent results on weighted polynomial approximationsfor functions defined on the real semiaxis. The function may grow exponentially both at $0$ and at $+\\infty$.We discuss orthogonal polynomials, polynomial inequalities, function spaces with new moduli of smoothness, estimates for the best approximation,Gaussian rules, and Lagrange interpolationwith respect to the weight w(x)=x^\\gamma\\mathrm{e}^{-x^{-\\alpha}-x^\\beta} ($\\alpha>0$, $\\beta>1$,$\\gamma\\geq 0$)