Minimum Norm Extremals in Function Spaces

Nonlinear minimization problems.- Minimization with linear operators.- Nonlinear operators in LP, 1<p??.- L? Minimization problems for elliptic operators.- L1 minimization in one and several variables.- Sets of uniqueness in L? minimization problems.- Bang-Bang optimal controls.- A general theorem of Kuhn-Tucker type.- Stable and unstable elastica equilibrium and the problem of minimum curvature.- Approximation by extremals of nonlinear differential expressions in one variable and quadratic forms in several variables.- The trigonometric and algebraic favard problem.- Minimization and interpolation at integer points of the real axis.- The Landau problem and Kolmogorov’s theorem.- Perfect interpolating splines on compact intervals.- A pólya algorithm for the favard solution, N-width characterizations and Whitney type theorems.- Application of the Riesz-Fredholm-Schauder theory to spline functions.- Epilogue.