  We propose a general theoretical description of chemical reactions occurring
on a catalytic surface with heterogeneous reactivity. The propagator of a
diffusion-reaction process with eventual absorption on the heterogeneous
partially reactive surface is expressed in terms of a much simpler propagator
toward a homogeneous perfectly reactive surface. In other words, the original
problem with general Robin boundary condition that includes in particular mixed
Robin-Neumann condition, is reduced to that with Dirichlet boundary condition.
Chemical kinetics on the surface is incorporated as a matrix representation of
the surface reactivity in the eigenbasis of the Dirichlet-to-Neumann operator.
New spectral representations of important characteristics of
diffusion-controlled reactions, such as the survival probability, the
distribution of reaction times, and the reaction rate, are deduced. Theoretical
and numerical advantages of this spectral approach are illustrated by solving
interior and exterior problems for a spherical surface that may describe either
an escape from a ball or hitting its surface from outside. The effect of
continuously varying or piecewise constant surface reactivity (describing,
e.g., many reactive patches) is analyzed.
