Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation
The paper deals with the search for effective moduli from ineffective uniqueness proofs of classical analysis. The author shows that, under suitable conditions, it is possible to extract an effective modulus of uniqueness from the proof. In particular this applies to the proof of uniqueness for the best Chebycheff approximation of \(f\in{\mathcal C}[0,1]\) by polynomials of degree \(\leq n\) given by de La Vallée Poussin, and provides explicit moduli of uniqueness and uniform constants of strong unicity.
ineffective uniqueness proofs of classical analysis
scientific article; zbMATH DE number 444823
scientific article