A Liouville Theorem for Matrix‐Valued Harmonic Functions on Nilpotent Groups | Zendy

Chu ChoHo | Zendy; Vu Tuan Giao | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

A Liouville Theorem for Matrix‐Valued Harmonic Functions on Nilpotent Groups

Author(s) -

Chu ChoHo,

Vu Tuan Giao

Publication year - 2003

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609303002169

Subject(s) - mathematics , nilpotent , bounded function , pure mathematics , harmonic function , degenerate energy levels , matrix (chemical analysis) , mathematical analysis , physics , quantum mechanics , materials science , composite material

Let σ be a non‐degenerate positive M n ‐valued measure on a locally compact group G with ‖σ‖ = 1. An M n ‐valued Borel function f on G is called σ‐harmonic if f ( x ) = ∫ G f ( x y − 1) d σ ( y )for all x ∈ G . Given such a function f which is bounded and left uniformly continuous on G , it is shown that every central element in G is a period of f . Further, it is shown that f is constant if G is nilpotent or central. 2000 Mathematics Subject Classification 31C05, 43A05, 45E10, 46G10.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research