Infinitely divisible representations and positive definite functions on a compact group
نویسندگان
چکیده
منابع مشابه
Conditionally Positive Definite Kernels and Infinitely Divisible Distributions
We give a precise characterization of two important classes of conditionally positive definite (CPD) kernels in terms of integral transforms of infinitely divisible distributions. In particular, we show that for any stationary CPD kernel A(x, y) = f(x − y), f is the log-characteristic function of a uniquely determined infinitely divisible distribution; further, for any additive CPD kernel A(x, ...
متن کاملRelations between positive definite functions and irreducible representations on a locally compact groupoid
If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...
متن کاملWeakly infinitely divisible measures on some locally compact Abelian groups
Let G be a locally compact Abelian topological group having a countable basis of its topology. We also suppose that G has the T0–property, that is, ⋂ U∈Ne U = {e}, where e denotes the identity element of G and Ne is the collection of all Borel neighbourhoods of e. (By a Borel neighbourhood U of e we mean a Borel subset of G for which there exists an open subset Ũ of G such that e ∈ Ũ ⊂ U.) Let ...
متن کاملIsotropic Infinitely Divisible Processes on Compact Symmetric Spaces
Let G be a connected compact Lie group, K a compact subgroup, such that G/K is a Riemannian symmetric homogeneous space. (See [l ] for terminology and notation.) We fix once and for all a G-invariant metric on G/K. D(G/K) will stand for the algebra of those differential operators on C°°(G/.K) which are invariant under the action of G. S(K\G/K) stands for the semi-group, under convolution as pro...
متن کاملPositive Positive-definite Functions and Measures on Locally Compact Abelian Groups
In the paper [1] we gave a cohomological interpretation of Tate’s Riemann-Roch formula using some new harmonic analysis objects, ghost-spaces. When trying to investigate these objects in general, we realized the importance of functions and measures on locally compact abelian groups that are both positive and positive-definite at the same time. It looks like this class of functions and measures ...
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: Communications in Mathematical Physics
سال: 1970
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf01646621