On normalizers and centralizers of compact Lie groups. Applications to structural probability theory

• Autorzy: Hazod W.
• Języki publikacji: EN

Abstrakty

EN

The concept of operator stability on finite-dimensional vector spaces V was generalized in the past into several directions. In particular, operator-semistable and self-decomposable laws and self-similar processes were investigated and the underlying vector space V may be replaced by a simply connected nilpotent Lie group G. This motivates investigations of certain linear subgroups of GL (V) and Aut (G), respectively, the decomposability group of a full probability μ and its compact normal subgroup, the invariance group. Using some basic properties of algebraic groups, the structure of normalizers and centralizers of compact matrix groups is analyzed and applied to the above-mentioned set-up, proving the existence and describing the shape of exponents and of commuting exponents of (operator-) semistable laws. Further applications are mentioned, in particular for operator self-decomposable laws and self-similar processes.

Słowa kluczowe

EN

exponent; commuting exponent; operator-semistable law; operator-stable law; normalizer; centralizer

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 1
• Strony: 39--60
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Hazod W.

• Department of Mathematics, University of Dortmund, D-44221 Dortmund, Germany

Bibliografia

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