Background

Lindelöf was born on March 7, 1870, in Helsinki, Finland, the son of the mathematician Leonard Lorenz Lindelöf, who was a professor in Heisingfors from 1857 to 1874. His brother was Uno Lorenz Lindelöf.

Education

Lindelöf studied at the University of Helsinki from 1887, where he completed his Doctor of Philosophy in 1893.

Career

In 1902 Lindelöf became assistant professor and in 1903 full professor of mathematics at the University of Helsinki. From 1907 he belonged to the editorial board of the Acta Mathematica, and he was a member of many learned academies and societies. He received honorary doctoral degrees from the Universities of Uppsala, Oslo, and Stockholm, and he was also named honorary professor by the University of Helsinki. He retired in 1938.

Lindelöf early abandoned creative scientific research and devoted himself enthusiastically to his duties as a professor; he was always available to researchers and colleagues. He laid the foundations for the study of the history of mathematics in Finland and trained many students. In an interesting festschrift published in honor of Lindelöf’s sixtieth birthday fourteen authors presented papers on function theory, diophantine equations, correlation theory, and number theory.

Lindelöf devoted his last years mainly to publishing textbooks which were noted for their lucidity and comprehensible style. Of his publications, eight deal with the theory of differential equations, twenty-three with function theory, four with the theory of error in harmonic analysis, and five with other fields.

Achievements

• Lindelöf is best known for the Picard-Lindelöf theorem on differential equations. He also developed the Phragmén-Lindelöf principle, one of several refinements of the maximum modulus principle that he proved in complex function theory.

Works

More photos

• book

  • Le Calcul Des Residus Et Ses Applications A La Theorie Des Fonctions

    (French Edition)

    1905

Views

At the beginning of his career Lindelöf published a remarkable work on the theory of differential equations, in which he investigated the existence of solutions (“Sur 1’intégration de l’équation differentielle de Kummer,” in Acta Societatis Scientiae Fennicae, 1890). He soon turned his attention to function theory, and in this area solved some fundamental problems in the theory of analytic functions. His primary field of interest, however, was in entire functions. He considered the mutual dependency between the growth of the function and the coefficients of the Taylor expansion. He also treated the behavior of analytic functions in the neighborhood of a singular point. The investigations concern questions which arise from Picard’s problem. Together with Phragmén he developed a general principle that he applied to function theory. His works are characterized by clarity and purity of method as well as elegance of form.

Lindelöf’s investigations of analytic continuation with the help of summation formulas had far-reaching results, which are set down in his excellent book Le calcul des résidus In it he examines the role which residue theory (Cauchy) plays in function theory as a means of access to modern analysis. In this endeavor he applies the results of Mittag-Lefiler. Moreover, he considers series analogous to the Fourier summation formulas and applications to the gamma function and the Riemann function. In addition, new results concerning the Stirling series and analytic continuation are presented. The book concludes with an asymptotic investigation of series defined by Taylor’s formula. The method of successive correction and the examination of this procedure following the studies of Picard and Schwarz is characteristic of Lindelöf’s work. His last works dealt with conformal mapping.

Membership

• Finnish Society of Sciences and Letters , Finland

• Royal Swedish Academy of Sciences , Sweden

Connections

Nothing is known of Lindelöf's family.

Father:

Lorenz Leonard Lindelöf

He published papers on minimal surfaces, the calculus of variations, differential geometry, mechanics, celestial mechanics and pension funds.

Brother:

Uno Lorenz Lindelöf

Student:

Lars Ahlfors

References

• Dictionary of Scientific Biography Volume 7
  1973