  The spectrum of interior transmission problem is the zero set of certain
entire functional determinant. It is classic that we deploy the series of
exponential polynomials to approximate the distribution of the roots of the
entire functions of exponential type. We construct an exponential system in the
form of $\{e^{ik_jr}\}$ according to the set of interior transmission
eigenvalues $\{k_{j}\}$. The eigenvalues are the zeros of a sine-type function.
In particular, they are intersection points of two asymptotically periodic
entire functions. The intersection set is asymptotically sine-like near the
real axis, so we may manage to construct a basis according to the class of
spectral objects. Due to the result of Paley-Wiener theorem, the zero set
generates a natural duality in the form of Fourier transform associated with
exponential polynomials. Whenever there is a sufficient quantity of
transmission eigenvalues, we are given a series of exponential polynomials to
saturate the functional density, which completes a $L^{2}$-Riesz basis in a
suitable ball.
