On take , and someone proposes three boundary conditions: y(0)=0, y(1)=0, y'(0)=0.…
PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Function spaces and operator theory
Conditions of Validity, Ch Sturm-Liouville theory: the spectral theorem for a differential operator
Problem
On [0,1] take Ly=−y′′, and someone proposes three boundary conditions: y(0)=0,y(1)=0,y′(0)=0. They compute the boundary form B(f,g)=[fg′−f′g]01 for two functions f,g satisfying all three conditions, find it vanishes, and conclude that (L,D) is a good self-adjoint Sturm-Liouville problem. Decide whether this conclusion is correct, and if not, say what has gone wrong.