Albrecht Böttcher

Technische Universität Chemnitz, Karl-Marx-Stadt, Saxony, Germany

Are you Albrecht Böttcher?

Claim your profile

Publications (4)1.14 Total impact

  • Albrecht Böttcher, Harald Heidler
    [Show abstract] [Hide abstract]
    ABSTRACT: Given a compact Hausdorff spaceX, we may associate with every continuous mapa: X X a composition operatorC a onC(X) by the rule(C a f)(x) = f(a(x)). We describe all self-mapsa for whichC a is an algebraic operator or an essentially algebraic operator (i.e. an operator algebraic modulo compact operators), determine the characteristic polynomialp a (z) and the essentially characteristic polynomialq a (z) in these cases and show how the connectivity ofX may be characterized in terms of the quotientsp a (z)/q a (z).
    Aequationes Mathematicae 01/1995; 49(1):276-294. · 0.42 Impact Factor
  • Albrecht Böttcher, Harald Heidler
    [Show abstract] [Hide abstract]
    ABSTRACT: The focus of this paper is on the following problem. Given a linear space F of complex-valued functions on a set X and a polynomial p(z), is there an algebraic composition operator on F whose characteristic polynomial equals p(z)? We show that the supply of all the polynomials p(z) for which the answer to this question is affirmative depends heavily on the structure of the space F.
    Integral Equations and Operator Theory 01/1992; 15(3):389-411. · 0.71 Impact Factor
  • Albrecht Böttcher, Harald Heidler
    [Show abstract] [Hide abstract]
    ABSTRACT: Let X be a compact Hausdorff space and Aut X the group of all homeomorphisms of X onto itself. Given two involutions α,β∈AutX (α 2 =e=β 2 ), let grp(α,β) be the smallest subgroup containing α and β. The aim of the paper is to find conditions for the unique solvability of ∑ g∈G a g ϕ(g(x))=f(x)(x∈X), where f∈C(X) is given, ϕ∈C(X) is the unknown function and G is a subset of grp(α,β). The case where grp(α,β) is finite has been dealt with by A. B. Antonevich [Linear functional equations: The operator theory approach (Russian), Univ. Press, Minsk (1988)]. Here the case is considered where grp(α,β) is infinite.
    Seminar Analysis. Operator Equations and Numerical Analysis. 01/1990;
  • Albrecht Böttcher, Harald Heidler
    [Show abstract] [Hide abstract]
    ABSTRACT: The focus of the talk is on the following problem. Given a linear space 𝔽 of complex-valued functions on a set 𝕏 and a polynomial p(z), is there an algebraic composition operator on 𝔽 whose characteristic polynomial equals p(z)?

Publication Stats

3 Citations
1.14 Total Impact Points

Institutions

  • 1992
    • Technische Universität Chemnitz
      Karl-Marx-Stadt, Saxony, Germany