English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we consider the \({\bar{\partial }}\)-problem in fiber bundles (fibers biholomorphic to \({\mathbb {C}}^k\), \(k\geqslant 1\)), namely the equation \({\bar{\partial }}\sigma =\omega \) for (0, 1)-forms \(\omega \) which decrease along the fibers. The order of decrease is slightly more than one. The important fact is that we do not assume that \(\omega \) has compact support. The main theorem says that the equation has a solution which also decreases along fibers, however, not necessarily with the order as the original form. Existence of solution of the above mentioned \({\bar{\partial }}\)-problem can be applied in various situations in Complex Analysis, in particular, to the Hartogs extension phenomenon.

$${\bar{\partial }}$$ ∂ ¯ -Problem in Fiber Bundles for Decreasing (0, 1)-Forms