On a generalization of the Lebesgue's constant

Highlights: • A Lebesgue's constant meaningful for polynomial interpolations of any field. • This generalization coincides with the known one for the scalar case. • The language of discrete exterior calculus is adopted. • This generalization is an absolute novelty. In this work we generalize the definition of the Lebesgue's constant to the case of field interpolation by high-order Whitney's forms on simplices. We underline the important theoretical concepts at play.