| Title:
|
The Laplace derivative (English) |
| Author:
|
Svetic, R. E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
331-343 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A function $f:\Bbb R \rightarrow \Bbb R$ is said to have the $n$-th Laplace derivative on the right at $x$ if $f$ is continuous in a right neighborhood of $x$ and there exist real numbers $\alpha_0, \ldots, \alpha_{n-1}$ such that $s^{n+1}\int_0^\delta e^{-st}[f(x+t)-\sum_{i=0}^{n-1}\alpha_i t^i/i!]\,dt$ converges as $s\rightarrow +\infty$ for some $\delta>0$. There is a corresponding definition on the left. The function is said to have the $n$-th Laplace derivative at $x$ when these two are equal, the common value is denoted by $f_{\langle n\rangle }(x)$. In this work we establish the basic properties of this new derivative and show that, by an example, it is more general than the generalized Peano derivative; hence the Laplace derivative generalizes the Peano and ordinary derivatives. (English) |
| Keyword:
|
Peano derivative |
| Keyword:
|
generalized Peano derivative |
| Keyword:
|
Laplace derivative |
| Keyword:
|
Laplace transform |
| Keyword:
|
Tauberian theorem |
| MSC:
|
26A21 |
| MSC:
|
26A24 |
| MSC:
|
26A48 |
| MSC:
|
40E05 |
| MSC:
|
44A10 |
| idZBL:
|
Zbl 1051.26004 |
| idMR:
|
MR1832151 |
| . |
| Date available:
|
2009-01-08T19:10:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119247 |
| . |
| Reference:
|
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| Reference:
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| . |
