Entanglement of Positive Definite Functions on Compact Groups
نویسندگان
چکیده
منابع مشابه
Positive 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 کاملQuaternion-valued positive definite functions on locally compact Abelian groups and nuclear spaces
In this talk we introduce and study quaternion-valued positive definite functions on locally compact Abelian groups, real countably Hilbertian nuclear spaces and on the space of countably infinite tuples of real numbers endowed with the Tychonoff topology. In particular, we prove a quaternionic version of the Bochner-Minlos theorem. We will see that in all these various settings the integral re...
متن کاملStability results for approximation by positive definite functions on compact groups
We consider interpolation methods defined by positive definite functions on a compact group. Estimates for the smallest and largest eigenvalue of the interpolation matrix in terms of the localization of the positive definite function on G are presented and we provide a method to get positive definite functions explicitly on compact semisimple Lie groups. Finally we apply our results to construc...
متن کاملExtensions of Positive Definite Functions on Amenable Groups
Let S be a subset of a amenable group G such that e ∈ S and S = S. The main result of the paper states that if the Cayley graph of G with respect to S has a certain combinatorial property, then every positive definite operator-valued function on S can be extended to a positive definite function on G. Several known extension results are obtained as a corollary. New applications are also presented.
متن کاملExtensions of Positive Definite Functions on Free Groups
An analogue of Krein’s extension theorem is proved for operatorvalued positive definite functions on free groups. The proof gives also the parametrization of all extensions by means of a generalized type of Szegö parameters. One singles out a distinguished completion, called central, which is related to quasi-multiplicative positive definite functions. An application is given to factorization o...
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: 2008
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-008-0493-6