Two More Counterexamples to the Infinite Dimensional Carleson Embedding Theorem

Takens’ embedding theorem for infinite-dimensional dynamical systems

Takens’ time delay embedding theorem is shown to hold for finitedimensional subsets of infinite-dimensional spaces, thereby generalising previous results which were only valid for subsets of finite-dimensional spaces: Let X be a subset of a Hilbert space with upper box-counting dimension d and ‘thickness exponent’ τ , which is invariant under a Lipschitz map Φ. Suppose that E , the set of all f...

A topological delay embedding theorem for infinite-dimensional dynamical systems

A time delay reconstruction theorem inspired by that of Takens (1981 Springer Lecture Notes in Mathematics vol 898, pp 366–81) is shown to hold for finite-dimensional subsets of infinite-dimensional spaces, thereby generalizing previous results which were valid only for subsets of finite-dimensional spaces. Let A be a subset of a Hilbert space H with upper box-counting dimension d(A) = d and ‘t...

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 ...

On Laplace–Carleson embedding theorems

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. The little Hankel operators on these Bergman spaces are also considered. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive h...

An Infinite Dimensional Convolution Theorem