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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The smoothness-increasing operator “convolution” is well known for inheriting the best properties of each parent function. It is also well known that if f  L and g is a Bounded Variation (BV) function, then f  g inherits the properties from the parent’s spaces. This aspect of BV can be generalized in many ways and many generalizations are obtained. However, in this paper we introduce the notion of p – Bounded variation function. In relation to that we show that the convolution of two functions f  g is the inverse Fourier transforms of the two functions. Moreover, we prove that if f, g  BV[0, 2], then f  g  BV[0, 2], and that on any locally compact Abelian group, a version of the convolution theorem holds.

On the Convolution of Functions of p – Bounded Variation and a Locally Compact Hausdorff Topological Group