Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces

Fixed Points of Multimaps Which Are Not Necessarily Nonexpansive

Let C be a nonempty closed bounded convex subset of a Banach space X whose characteristic of noncompact convexity is less than 1 and T a continuous 1-χ-contractive SL map (which is not necessarily nonexpansive) from C to KC(X) satisfying an inwardness condition, where KC(X) is the family of all nonempty compact convex subsets of X . It is proved that T has a fixed point. Some fixed points resul...

An Index for Set-valued Maps in Infinite- Dimensional Spaces

Previous fixed point indexes defined for a set-valued map in an infinite-dimensional space have required the values of this map to be convex sets. The corresponding assumption of this paper is that the values be (co-)acyclic sets, i.e., that the reduced Alexander cohomology group of each of these sets be trivial in each dimension. Other assumptions are that the space is locally convex and that ...

Total subspaces in dual Banach spaces which are not norming over any infinite dimensional subspace

Total subspaces in dual Banach spaces which are not norming over any infinite dimensional subspace Abstract. The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite dimensional subspace of X if and only if X has a nonquasireflexive quotient space with the strictly singular quotient mapping. Let X be a Banach space and X * be its dua...

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 ...