On an extremal problem

Krystyna Zyskowska

Displaying similar documents to “On an extremal problem”

Linear integral equations in the space of regulated functions

Milan Tvrdý (1998)

Mathematica Bohemica

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n this paper we investigate systems of linear integral equations in the space $𝔾_{L}^{n}$ of $n$ -vector valued functions which are regulated on the closed interval $[0, 1]$ (i.e. such that can have only discontinuities of the first kind in $[0, 1]$ ) and left-continuous in the corresponding open interval $(0, 1) .$ In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where $f \in 𝔾_{L}^{n}$ , the columns of the $n \times n$ -matrix valued function $A$ belong to $𝔾_{L}^{n}$ , the entries of $B (t, .)$ have a bounded variation...

On the set of solutions of the system $x_{1} + x_{2} + x_{3} = 1, x_{1} x_{2} x_{3} = 1$

Miloslav Hlaváček (1998)

Mathematica Bohemica

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A proof is given that the system in the title has infinitely many solutions of the form $a_{1} + a_{2}$ , where $a_{1}$ and $a_{2}$ are rational numbers.

Hardy inequalities in function spaces

Hans Triebel (1999)

Mathematica Bohemica

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Let $Ω$ be a bounded $C^{\infty}$ domain in $ℝ^{n}$ . The paper deals with inequalities of Hardy type related to the function spaces $B_{p q}^{s} (Ω)$ and $F_{p q}^{s} (Ω)$ .

On $(j, k)$ -symmetrical functions

Piotr Liczberski, Jerzy Połubiński (1995)

Mathematica Bohemica

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n the present paper the authors study some families of functions from a complex linear space $X$ into a complex linear space $Y$ . They introduce the notion of $(j, k)$ -symmetrical function ( $k = 2, 3, \dots$ ; $j = 0, 1, \dots, k - 1$ ) which is a generalization of the notions of even, odd and $k$ -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset $U$ of $X$ can be uniquely represented as the sum of an even function and an odd function.

Displaying similar documents to “On an extremal problem”

Linear integral equations in the space of regulated functions

On the set of solutions of the system x 1 + x 2 + x 3 = 1 , x 1 x 2 x 3 = 1

Hardy inequalities in function spaces

On ( j , k ) -symmetrical functions

On the set of solutions of the system $x_{1} + x_{2} + x_{3} = 1, x_{1} x_{2} x_{3} = 1$

On $(j, k)$ -symmetrical functions