0-1-sequences of Toeplitz type

  • Konrad Jacobs
  • Michael Keane
Article

Summary

0-1-sequences are constructed by successive insertion of a periodic sequence of symbols 0, 1 and “hole” into the “holes” of the sequence already constructed. Assuming that finally all “holes” are filled with symbols 0, 1, an almost periodic point in shift space results. Under certain conditions, it is even strictly ergodic. It is proved that the attached invariant measure has pure point spectrum, and a rather explicit expression for eigenvectors is obtained.

Keywords

Stochastic Process Probability Theory Explicit Expression Invariant Measure Mathematical Biology 

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References

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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Konrad Jacobs
    • 1
  • Michael Keane
    • 2
  1. 1.Mathematisches Institut der UniversitÄt Erlangen-NürnbergErlangen
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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