The Cauchy-Riemann Operator in Infinite-Dimensional Spaces

The Cauchy-Riemann Operator in Infinite Dimensional Spaces

In this survey article we present a sketch of the tecliniques which allowed to advance into the problem of solving the a-problem in infinite dimensional spaces. As an example we show how tite O-problem for a holomorphic (O,2)-form on a D.F.N. space can be solved by using the solution of the a-problem for a holomorphic (O,2)-form on a separable Hilbert space. For further detajís we refer to SORA...

On Three-dimensional Cauchy-riemann Manifolds

of the almost complex tensor of C2 ("multiplication by i "). The collection of these subspaces HpM forms a bundle H MeT M called the horizontal or contact bundle. (Indeed, strict pseudoconvexity of M implies that the plane field {HpM} is nondegenerate, i.e. defines a contact structure.) The almost complex tensor of C2 then restricts to a bundle endomorphism J : H M -+ H M such that J2 = -id. Th...

$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

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 ...