On differentiable and monogenic functions in a harmonic algebra
For locally bounded and differentiable in the sense of G\^ateaux functions $\Phi$ given in a three-dimensional commutativeharmonic algebra with two-dimensional radical, we prove the following statement: if the function $\Phi$ domain is convex "in the radical direction" and the diff...
Saved in:
| Date: | 2017 |
|---|---|
| Author Affiliations: |
|
| Keywords: | keywords |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2017
|
| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/114 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
| Download file: |
|
Institution
Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | For locally bounded and differentiable in the sense of G\^ateaux functions $\Phi$ given in a three-dimensional commutativeharmonic algebra with two-dimensional radical, we prove the following statement: if the function $\Phi$ domain is convex "in the radical direction" and the difference $\zeta_1-\zeta_2$ belongs to the radical, the difference $\Phi(\zeta_1)-\Phi(\zeta_2)$ belongs also to the radical. As a result, we prove that locally bounded and differentiable in the sense of G\^ateaux functions are also differentiable in the sense of Lorch. |
|---|