@misc{PickenhainBurtchen, author = {Pickenhain, Sabine and Burtchen, Angie}, title = {Problems in the Calculus of Variations on Unbounded Intervals—Fourier-Laguerre Analysis and Approximations}, series = {Vietnam Journal of Mathematics}, volume = {47}, journal = {Vietnam Journal of Mathematics}, number = {3}, issn = {2305-221X}, doi = {10.1007/s10013-019-00349-3}, pages = {617 -- 638}, abstract = {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.}, language = {en} }