Yalmar Mellin (full name Robert Jalmar Mellin , fin. Robert Hjalmar Mellin , June 19, 1854, Liminka , Grand Duchy of Finland - April 5, 1933, Helsinki , Finland ) - Finnish mathematician, expert in the theory of functions, who developed one of the most famous integral transformations named after him is the Mellin transform .
| Yalmar Mellin | |
|---|---|
| Hjalmar mellin | |
 Robert Yalmar Mellin | |
| Date of Birth | June 19, 1854 |
| Place of Birth | Liminka , Grand Duchy of Finland (now Finland ) |
| Date of death | April 5, 1933 (78 years) |
| Place of death | Helsinki , Finland |
| A country |  Grand Duchy of Finland →  Finland |
| Scientific field | maths |
| Place of work | |
| Alma mater | Alexandrovsky University (1840) |
| supervisor | Gösta Mittag-Leffler |
| Famous students | Ernst Lindelöf [1] |
Biography
Yalmar Mellin was born on June 19, 1854 in Liminka , in Northern Ostrobothnia , just south of the city of Oulu , about 600 km north of Helsinki . His father was a priest. Yalmar Mellin grew up and received school education in the city of Hämeenlinna , about 100 km north of Helsinki , and then entered the Imperial Alexander University , where his teacher was the famous mathematician Gösta Mittag-Leffler [2] .
In the fall of 1881, he defended his thesis on the algebraic functions of one complex variable . After that, twice, in 1881 and 1882, he traveled to Berlin to work under the direction of Karl Weierstrass , and in 1883-1884 he came to Stockholm to continue working with Gösta Mittag-Leffler . From 1884 to 1891, he was an associate professor at Stockholm University , but did not give any lectures [2] .
Also in 1884, he was appointed senior lecturer at the newly established Helsinki Polytechnic Institute . In 1904-1907 he was the rector of this institute, and from 1907 he worked as a professor of mathematics, until his retirement in 1926 [2] .
Member of the Finnish Academy of Sciences (1908) [3] .
Scientific Results
A significant part of Yalmar Mellin's research is related to the development and use of the integral transform , which was given his name — the Mellin transform [4] . The core of the Mellin integral transform is a power function , and the Mellin transform on function defined as
- .
The inverse Mellin transform is given by the formula
- ,
where integration is carried out along a vertical straight line in the complex plane of the variable s , and the choice of a real parameter c must satisfy certain conditions specified in .
Notes
- ↑ Robert Hjalmar Mellin (HTML). Mathematics Genealogy Project, Department of Mathematics, North Dakota State University. The appeal date is August 22, 2012. Archived October 29, 2012.
- ↑ 1 2 3 R. Paris. Robert Hjalmar Mellin (HTML). School of Mathematics and University of St. Petersburg Andrews, Scotland. The appeal date is August 22, 2012. Archived October 29, 2012.
- ↑ Correspondence of S. V. Kovalevskaya and G. Mittag-Leffler. (Scientific Heritage, Volume 07). - M .: Science, 1984. - p. 299
- ↑ Eric W. Weisstein. Mellin Transform (HTML). MathWorld - mathworld.wolfram.com. The appeal date is August 22, 2012.