A constrained Nevanlinna-Pick interpolation problem Kenneth DavidsonVern PaulsenMrinal RaghupathiDinesh Singh 47A57Nevanlinna-Pick interpolationreproducing kernels We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $f'(0) = 0$. Alternatively, these results can be interpreted as interpolation results for $H^{\infty}(V)$, where $V$ is the intersection of the bidisk with an algebraic variety. We use an analysis of C*-envelopes to show that these same conditions do not suffice for matrix interpolation. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3486 10.1512/iumj.2009.58.3486 en Indiana Univ. Math. J. 58 (2009) 709 - 732 state-of-the-art mathematics http://iumj.org/access/