Abstract
For the r-adic one-dimensional maps, the author explicitly constructs the decaying eigenstates and adjoint eigenstates associated with the Ruelle resonances. It is shown that the eigenfunctions of the corresponding Frobenius-Perron operator are the well known Bernoulli polynomials. The adjoint eigendistributions are obtained as derivatives of the Dirac distributions at the end points of the unit interval. The resulting expansion of the initial density in terms of the decaying eigenstates is given by the Euler summation formula.