Pointwise Convergence of Fourier-type Series with Exponential Weights

Abstract

Let $\mathbb{R}=(-\infty ,\infty )$, and let $Q\in C^1(\mathbb{R}):\mathbb{R}\to [0,\infty )$ be an even function. We consider the exponential weights $w(x)=e^{-Q(x)}$, $x\in \mathbb{R}$. In this paper we obtain a pointwise convergence theorem for the Fourier-type series with respect to the orthonormal polynomials $\left\{p_n(w^2;x)\right\}$.