A rank theorem for infinite dimensional spaces

On the convolution theorem for infinite-dimensional parameter spaces

In this paper we give examples which show that the convolution theorem (Boll, [1], Hajek, [2]) cannot be extended to infinite-dimensional shift experiments. This answers a question posed by van der Vaart, [9], and which has been considered also by LeCam, [5].

Infinite dimensional non-positively curved symmetric spaces of finite rank

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.

The Failure of Rolle’s Theorem in Infinite-dimensional Banach Spaces

We prove the following new characterization of C (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a C smooth (Lipschitz) bump function if and only if it has another C smooth (Lipschitz) bump function f such that its derivative does not vanish at any point in the interior of the support of f (that is, f does not satisfy Rolle’s theorem). Moreover, the support o...

Infinite dimensional Teichmüller spaces

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 ...