Person: Kellogg, Oliver Dimon
Oliver Kellogg was an American mathematician best known for his work on potential theory.
Mathematical Profile (Excerpt):
- Day Otis Kellogg was also important as the American editor of Encyclopaedia Britannica.
- Oliver studied as an undergraduate at Princeton University, entering in 1895.
- After receiving his A.B. in 1899, Kellogg continued his studies for a Master's Degree at Princeton.
- Kellogg spent the year 1900-01 at the University of Berlin, then moved to Göttingen where he spent 1901-02 working for his doctorate.
- Fredholm had just published a major work on the Dirichlet problem but Fredholm's methods did not apply to the regions which Hilbert suggested Kellogg investigate.
- In 1902 Kellogg published his first paper giving a direct proof of Fredholm's inversion formula.
- However Kellogg soon became less than happy with these papers.
- Secondly some of Kellogg's results were incomplete and others were incorrect.
- Kellogg was appointed to the University of Missouri in 1905 where, despite a heavy teaching and administrative load he was able to publish impressive papers on potential theory.
- This paper includes what today is called 'Kellogg's theorem' on harmonic and Green's functions.
- Although he would return to potential theory, Kellogg next published a number of papers on sets of real orthogonal functions.
- Kellogg published the paper Invariant points in function space jointly with G D Birkhoff in 1922.
- This contains the Birkhoff-Kellogg Theorem which generalises the Brouwer fixed point theorem.
- Kellogg published the classic text Foundations of potential theory in 1929 (it was reprinted in 1967).
- While not specifically mentioned, many of the proofs in the volume - even of well-known results - are original and due to Kellogg himself.
- This volume also includes the first statement of the celebrated Kellogg-Evans Lemma (proven in generality by Griffith C Evans in 1933).
- Kellogg also wrote a number of papers on the existence of certain sets of functions in analysis as well as generalisations of polynomials due to Sergei Bernstein.
- Kellogg continued to work at Harvard until his death which resulted from a heart attack which he suffered while climbing near Greenville, Maine.
- The full story of Kellogg's many successful efforts to help others would be an extraordinary one ...
Born 10 July 1878, Linwood, Pennsylvania, USA. Died 26 July 1932, Greenville, Maine, USA.
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Thank you to the contributors under CC BY-SA 4.0!
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive