Minimum Norm Extremals in Function Spaces: With Applications to Classical and Modern Analysis

Introduction....Pages 1-11
Nonlinear minimization problems....Pages 12-22
Minimization with linear operators....Pages 23-32
Nonlinear operators in L P , 1<p≤∞....Pages 33-46
L ∞ Minimization problems for elliptic operators....Pages 47-53
L 1 minimization in one and several variables....Pages 54-63
Sets of uniqueness in L ∞ minimization problems....Pages 64-72
Bang-Bang optimal controls....Pages 73-84
A general theorem of Kuhn-Tucker type....Pages 85-89
Stable and unstable elastica equilibrium and the problem of minimum curvature....Pages 90-106
Approximation by extremals of nonlinear differential expressions in one variable and quadratic forms in several variables....Pages 107-133
The trigonometric and algebraic favard problem....Pages 134-150
Minimization and interpolation at integer points of the real axis....Pages 151-163
The Landau problem and Kolmogorov’s theorem....Pages 164-171
Perfect interpolating splines on compact intervals....Pages 172-176
A pólya algorithm for the favard solution, N-width characterizations and Whitney type theorems....Pages 177-194
Application of the Riesz-Fredholm-Schauder theory to spline functions....Pages 195-205
Epilogue....Pages 206-207