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 ∈ 𝔾 L n , the columns of the n × n -matrix valued function A belong to 𝔾 L n , the entries of B ( t , . ) have a bounded variation...

Hardy inequalities in function spaces

Hans Triebel (1999)

Mathematica Bohemica

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Let Ω be a bounded C ∞ 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 , ⋯ ; j = 0 , 1 , ⋯ , 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.