Almost periodic oscillations of suspended string under quasiperiodic linear force

We shall be concerned with the behavior of a suspended string to which a time-periodic or time-quasiperiodic outer force works. We shall deal with IBVP for a linear equation of a suspended string, and show that every solution is almost periodic in time. The result shall be shown under the assumptions that the basic periods (the period), the length of the string and the zero points of the Bessel functions of the first kind satisfy the Diophantine type number-theoretic condition and the forcing term is smooth. In order to deal with the problems we shall develop some well-matched function spaces and solve the eigenvalue problem for suspended string operator.