Abstract
Let (A(a)u)(x) := ∫ a 0 (1 − xt)−1u(t) dt, 0 < a < 1 . Properties of the operators A(a) as a → 1 are studied. It is proved that A := A(1) is a bounded, positive self-adjoint operator in H = L2[0, 1] , ||A|| π , while A : C(0, 1) → C(0, 1) is unbounded. Mathematics subject classification (1991): 35R30.
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