Quasi-invariance and analyticity of measures on compact groups
نویسندگان
چکیده
منابع مشابه
Disintegration of Measures on Compact Transformation Groups
To prove 1.1, one first assumes X is compact and G is a Lie group. In this case, X is "measure-theoretically" the product Y x G; this follows from the existence of local cross-sections to the projection n [6]. Let n2 : X ~ Y x G —> G, and define a map £ from L(Y, v) to the space of Radon measures on G as follows: £(ƒ) = TÏ2 [if ° n) ' M] • Apply the Dunford-Pettis Theorem [3] to ? to obtain a m...
متن کاملQuasi-invariance for Heat Kernel Measures on Sub-riemannian Infinite-dimensional Heisenberg Groups
We study heat kernel measures on sub-Riemannian infinitedimensional Heisenberg-like Lie groups. In particular, we show that Cameron-Martin type quasi-invariance results hold in this subelliptic setting and give L-estimates for the Radon-Nikodym derivatives. The main ingredient in our proof is a generalized curvature-dimension estimate which holds on approximating finite-dimensional projection g...
متن کاملConditional Haar Measures on Classical Compact Groups
We give a probabilistic proof of the Weyl integration formula on U(n), the unitary group with dimension n. This relies on a suitable definition of Haar measures conditioned to the existence of a stable subspace with any given dimension p. The developed method leads to the following result: for this conditional measure, writing Z (p) U for the first nonzero derivative of the characteristic polyn...
متن کاملHua-pickrell Measures on General Compact Groups
Take a generic subgroup G, endowed with its Haar measure, from U(n,K), the unitary group of dimension n over the field K of real, complex or quaternion numbers. We give some equalities in law for Z := det(Id − G), G ∈ G : under some general conditions, Z can be decomposed as a product of independent random variables, whose laws are explicitly known (Section 2). Consequently G, endowed with a ge...
متن کاملA Quasi-invariance Theorem for Measures on Banach Spaces
We show that for a measure -y on a Banach space directional different ¡ability implies quasi-translation invariance. This result is shown to imply the Cameron-Martin theorem. A second application is given in which 7 is the image of a Gaussian measure under a suitably regular map.
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: Acta Mathematica
سال: 1963
ISSN: 0001-5962
DOI: 10.1007/bf02391812