On a parameter-based asymptotics of solutions to differential equations with coefficients from L-2(a, b)

摘要

The classical large-parameter asymptotic formulas for solutions to ordinary linear differential equations, which go back to Birkhoff, Langer, and Tamarkin, were derived for smooth coefficients. The smoothness conditions were relaxed in [1]. This paper considers the unstudied case of coefficients belonging to the space L2(a,b) and gives an exact characteristic of the asymptotic approximation. This case is particularly important from the point of view of operator theory [2].