Operator Norms of Powers of the Volterra Operator
Copyright policy )Operator Norms of Powers of the Volterra Operator
Let \(V: L^2[0,1]\to L^2[0, 1]\) be the Volterra operator defined by \(Vf(x)= \int^x_0 f(t) dt\). In the paper is proved that \(\lim_{m\to\infty} \|m!V^m\|={1\over 2}\). To obtain this, some more general results for the operator \(A: L^2[0,1]\to L^2[0,1]\) defined by \(Af(x)= \int^x_0 a(x- t) f(t) dt\), wehre \(a\) is a nonnegative, nondecreasing \(L^2\)-integrable function on \([0,1]\), are proved.
- Lancaster University United Kingdom
- Lancaster University Ghana Ghana
Integral operators, Volterra operator, Volterra integral equations, Linear operators on function spaces (general), Norms (inequalities, more than one norm, etc.) of linear operators
Integral operators, Volterra operator, Volterra integral equations, Linear operators on function spaces (general), Norms (inequalities, more than one norm, etc.) of linear operators
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