scholarly journals Fourier transform of $L^{p}$ on real rank 1 semisimple Lie groups

1982 ◽  
Vol 34 (4) ◽  
pp. 561-579 ◽  
Author(s):  
Takeshi KAWAZOE
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Real Rank ◽  
Semisimple Lie Groups

scholarly journals A qualitative uncertainty principle for semisimple Lie groups

1988 ◽  
Vol 45 (1) ◽  
pp. 127-132 ◽  
Author(s):  
Michael Cowling ◽  
John F. Price ◽  
Alladi Sitaram
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Uncertainty Principle ◽  
Finite Measure ◽  
Semisimple Lie Groups ◽  
Qualitative Uncertainty

AbstractRecently M. Benedicks showed that if a function f ∈ L2(Rd) and its Fourier transform both have supports of finite measure, then f = 0 almot everywhere. In this paper we give a version of this result for all noncompact semisimple connected Lie groups with finite centres.

Whittaker Functions on Real Semisimple Lie Groups of Rank Two

2010 ◽  
Vol 62 (3) ◽  
pp. 563-581 ◽  
Author(s):  
Taku Ishii
Keyword(s):  
Lie Groups ◽  
Principal Series ◽  
Real Rank ◽  
Whittaker Functions ◽  
Semisimple Lie Groups ◽  
Explicit Formulas ◽  
Series Representations ◽  
Principal Series Representations

AbstractWe give explicit formulas forWhittaker functions on real semisimple Lie groups of real rank two belonging to the class one principal series representations. By using these formulas we compute certain archimedean zeta integrals.

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