  This paper is concerned with inverse spectral problems for higher-order ($n >
2$) ordinary differential operators. We develop an approach to the
reconstruction from the spectral data for a wide range of differential
operators with either regular or distribution coefficients. Our approach is
based on the reduction of an inverse problem to a linear equation in the Banach
space of bounded infinite sequences. This equation is derived in a general form
that can be applied to various classes of differential operators. The unique
solvability of the linear main equation is also proved. By using the solution
of the main equation, we derive reconstruction formulas for the differential
expression coefficients in the form of series and prove the convergence of
these series for several classes of operators. The results of this paper can be
used for constructive solution of inverse spectral problems and for
investigation of their solvability and stability.
