Sharp asymptotics of the Kolmogorov entropy for Gaussian measures

Let U denote the unit ball of the Cameron–Martin space of a Gaussian measure on a Hilbert space. The sharp asymptotics for the Kolmogorov (metric) entropy numbers of U is derived. The condition imposed is regular variation of the eigenvalues of the covariance operator. A consequence is a precise link including constants to the functional quantization problem.