Representations of the Infinite-Dimensional Affine Group

Infinite-dimensional Group Representations

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

The size of infinite-dimensional representations

An infinite-dimensional representation π of a real reductive Lie group G can often be thought of as a function space on some manifold X. Although X is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of X. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and...

On the Form of the Finite-dimensional Projective Representations of an Infinite Abelian Group

If the locally compact abelian group G has a finitedimensional unitary irreducible projective representation with factor system co (i.e. G has an a>-rep), then a subgroup G(co) is defined which fulfils three roles. First, the square-root of the index of G(u)) in G is the dimension of every co-rep. Secondly, the co-reps of G can be labelled by the dual group of G(co), up to unitary equivalence. ...

Infinite-dimensional Representations of Real Reductive Groups

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...