Abstract
Model-independent constraints on the Isgur-Wise function and its derivatives, based on analyticity, unitarity, and perturbative QCD expansion for the polarization function in the spacelike region, are derived using a duality theorem in functional optimization. In particular, we obtan the allowed domain for the slope and the convexity of this function at zero recoil, using as input various information about the \ensuremath{\Upsilon} poles below the BB\ifmmode\bar\else\textasciimacron\fi{} threshold. The results are of interest for testing specific models of the heavy meson form factors and the extraction of the matrix element ${\mathit{V}}_{\mathit{c}\mathit{b}}$ from experimental data on exclusive semiliptonic decays of the B mesons.
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