TY - GEN A1 - Pickenhain, Sabine A1 - Burtchen, Angie T1 - Problems in the Calculus of Variations on Unbounded Intervals—Fourier–Laguerre Analysis and Approximations T2 - Vietnam Journal of Mathematics N2 - In this paper, we consider a class of variational problems on an unbounded interval of the real axis. This type of problems arises, e.g., in quantum mechanics and asymptotic controllability. The problem is treated in a Hilbert space setting with uniformly and non-uniformly weighted Sobolev spaces as state spaces. We provide sufficient conditions that a function from a weighted Sobolev space can be expanded into a Fourier–Laguerre series converging together with its distributional derivative pointwisely and uniformly. With this result, the considered variational problem is transformed into a problem in the sequence space of Fourier–Laguerre coefficients. We develop a Fourier–Laguerre method in these spaces in order to construct a polynomial approximation scheme for the solution of this problem. Y1 - 2019 U6 - https://doi.org/10.1007/s10013-019-00349-3 SN - 2305-221X SN - 2305-2228 VL - 47 IS - 3 SP - 617 EP - 638 ER -