Displaying similar documents to “Fractional integrals on spaces of homogeneous type”

Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions

Štefan Schwabik (2000)

Mathematica Bohemica

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This paper is a continuation of []. In [] results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) were presented. The Kurzweil type Stieltjes integration in the setting of [] for Banach space valued functions was used. Here we consider operator valued solutions of the homogeneous problem (t) = I +dt [A(s)](s) as well as the variation-of-constants formula for the former equation.

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

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From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra ¯ of generalized real numbers. It is worth mentioning that the algebra ¯ is not a field.