Stable Summation Methods for a Class of Singular Sturm-Liouville Expansions
Stable Summation Methods for a Class of Singular Sturm-Liouville Expansions
Given the Sturm-Liouville eigenfunction expansion of an ${L_2}$ function $f(x)$, summability theory provides means for recovering the value of $f({x_0})$ at points ${x_0}$ where $f$ is sufficiently regular. If the coefficients in the expansion are perturbed slightly (in the ${L_2}$ norm), a stable summation method will recover from the perturbed …