## On Differential Equations of Sturm-Liouville Type on a Half-axis |

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absolutely integrable analytic function Banach space Bochner's theorem boundary conditions bounded function boundedness c,A c,A Chapter complex conjugate continuous and let continuous function coordinate defined denote eigen-function exists a constant fact family of operators finite interval follows immediately formula func t ions function p(x function w(t,x,y functional equation functions 4>(x,k functions g Furthermore generalisation Green's formula half-axis Hence inequality interval A,A left-hand side Let us write linear combinations linear operator maximal ideal Mq necessary and sufficient nilpotent non-negative normed ring number of zeros obtain OO 0O operation Mq operator T^ff Pf is bounded Plancherel's theorem proof of Lemma proved q,Vq Riemann's function right-hand side satisfies the equation satisfy the conditions sense of Lebesgue sequence sufficiently large suppose tends to zero tion Translator's note twice differentiable values vanish identically whole axis y)dt zero with h