A differentiation operator with nonregular boundary conditions (Q1390458)

The differentiation operator \(L\) on \(L_p(0,1)\) with some boundary conditions is discussed . The author separates out some classes of nonregular boundary conditions, and gives a sharp estimate for the resolvent \((L-\lambda I)^{-1}\) with respect to the norm \(| \text{arg }\lambda| <\pi-\varepsilon\), \(| \lambda| \geq R_{\varepsilon}>0\), for some \(\varepsilon>0\).