Displaying similar documents to “Closed convex $l$-subgroups and radical classes of convergence $l$-groups”

Convergence l -groups with zero radical

Ján Jakubík (1997)

Mathematica Bohemica

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In this paper we investigate abelian convergence ℓ -groups with zero radical such that each bounded sequence has a convergent subsequence.

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...

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator ℓ ( y ) ≡ 1 w ( t ) ( r ( t ) y ) , t ∈ [ a , ∞ ) are established. These conditions are based on a recently proved relationship between spectral properties of ℓ and oscillation of a certain associated second order differential equation.