Abstract: | We consider the Tikhonov regularizer fλ of a smooth function f ε H2m[0, 1], defined as the solution (see [1]) to We prove that if f(j)(0) = f(j)(1) = 0, J = m, …, k < 2m − 1, then ¦f − fλ¦j2 Rλ(2k − 2j + 3)/2m, J = 0, …, m. A detailed analysis is given of the effect of the boundary on convergence rates. |