Minimum Norm Extremals in Function Spaces

Inhaltsverzeichnis

• 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.