Displaying similar documents to “On consequences of certain boundary conditions on the unit circle”

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.

Transitivity and partial order

Jiří Klaška (1997)

Mathematica Bohemica

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In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary n -element set up to n = 14 .

Reflected double layer potentials and Cauchy's operators

Dagmar Medková (1998)

Mathematica Bohemica

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Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.