Primary ideals at \(\infty\) are investigated in Beurling-type Fréchet algebras in the quasianalytic case. They are described by two parameters characterizing the rate of decay of their Fourier transforms at \(\pm\infty\). The so-called generalized Fourier transform is applied to treat related convolution equations. A necessary and sufficient condition for the orthogonality of a functional with empty spectrum and an ideal generated by a function is given in terms of their Fourier transforms. Beside that, the technique of asymptotically holomorphic functions is employed to describe asymptotics of quasianalytically smooth functions and to prove an extension of Levinson's log-log theorem.