CONTENTS 0. Introduction...........................................................................................5 1. Extrema of functionals in $H^ω[a,b]$ and perfect ω-splines................11 2. Auxiliary results...................................................................................22 3. Formulation of the main result.............................................................25 4. Proof of the main result.......................................................................32 5. The extrapolation problem...................................................................54 6. Maximization of functionals in $H^ω[a₁,a₂]$, -∞ ≤ a₁ < a₂ ≤ ∞..............56 7. Euler ω-splines on the finite interval....................................................62 Appendix A. Construction of Chebyshev splines.....................................68 Appendix B. Construction of Zolotarev splines........................................70 References.............................................................................................78
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