A complete analogue of Hardy's theorem on semisimple Lie groups

• Autorzy: Rudra P. Sarkar
• Języki publikacji: EN

Abstrakty

EN

A result by G. H. Hardy ([11]) says that if f and its Fourier transform f̂ are $O(|x|^m e^{-αx²})$ and $O(|x|ⁿ e^{-x²/(4α)})$ respectively for some m,n ≥ 0 and α > 0, then f and f̂ are $P(x)e^{-αx²}$ and $P'(x)e^{-x²/(4α)}$ respectively for some polynomials P and P'. If in particular f is as above, but f̂ is $o(e^{-x²/(4α)})$, then f = 0. In this article we will prove a complete analogue of this result for connected noncompact semisimple Lie groups with finite center. Our proof can be carried over to the real reductive groups of the Harish-Chandra class.

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups
• 22E46: Semisimple Lie groups and their representations
• 22E30: Analysis on real and complex Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 93
• Numer: 1
• Strony: 27-40

Daty

wydano

2002

Twórcy

autor

Rudra P. Sarkar

• Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India

Identyfikatory

DOI

10.4064/cm93-1-4