A quick proof of Harish-Chandra’s Plancherel theorem for spherical functions on a semisimple Lie group
نویسندگان
چکیده
منابع مشابه
An Lp-Lq version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups
We consider a real semisimple Lie group G with finite center and K a maximal compact subgroup of G. We prove an Lp −Lq version of Hardy’s theorem for the spherical Fourier transform on G. More precisely, let a, b be positive real numbers, 1 ≤ p, q ≤ ∞, and f a K-bi-invariant measurable function on G such that h−1 a f ∈ Lp(G) and eb‖λ‖ (f )∈ Lq(a∗ +) (ha is the heat kernel on G). We establish th...
متن کاملLivšic’s theorem for semisimple Lie groups
In this paper we show that strong generalizations of the measurable Livšic theorem for cocycles taking values in connected non-compact linear semisimple Lie groups, a canonical example being SL(2,R), can be deduced from an elegant approach of Brin and Pesin to the dynamics of partially hyperbolic systems.
متن کاملOn the Characters of a Semisimple Lie Group
where dx is the Haar measure of G and C?(G) is the set of all (complexvalued) functions on G which are everywhere indefinitely differentia t e and which vanish outside a compact set. V is called the Gârding subspace of § . Let R and C be the fields of real and complex numbers respectively and g0 the Lie algebra of G. We complexify g0 to Q and denote by $8 the universal enveloping algebra of Q [...
متن کاملA Quick Proof of the Pcf Theorem
The following note provide a short proof of Shelah’s pcf theorem via the new Theorem 7 below. The following theorems are used: (1) Shelah’s theorem on the existence of stationary sets in I[λ]; (2) Shelah’s trichotomy theorem; (3) the characterization [2] of sequences with exact upper bounds. A proof of Shelah’s trichotomy theorem is in [3],II,1.2 and a shorter proof is in the appendix to [2]. T...
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0507231-8