Abstract:
We study a system of polynomials orthonormal with respect to a Sobolev-type inner product and associated with classical Hermite polynomials. It is shown that for functions from a weighted Sobolev space the Fourier series in this system converges uniformly on an interval provided that the parameter $p$ is not less than two. For the cases where $p$ is less than two, we construct an example of a function whose Fourier series diverges at a given point. We also investigate the question of absolute convergence of the Fourier series in this system of polynomials on an interval.
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