Ernst Leonard Lindelöf (; 7 March 1870 – 4 June 1946) was a Finnish mathematician, who made contributions in

real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include co ...

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

and

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

Lindelöf space In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. The Lindelöf property is a weakening of the more commonly used notion of ''compactness'', which requires the existence of a ''finite'' sub ...

s are named after him. He was the son of mathematician

Lorenz Leonard Lindelöf Lorenz Leonard Lindelöf (13 November 1827, Karvia, Finland – 3 March 1908, Helsinki) was a Finnish mathematician, astronomer and politician. Biography Lindelöf grew up in a poor family. He learned German and French and studied astronomy and ...

and brother of the

philologist Philology () is the study of language in oral and written historical sources. It is the intersection of textual criticism, literary criticism, history, and linguistics with strong ties to etymology. Philology is also defined as the study of ...

. He was secretary of the Finnish Society of Science and Letters (societas scientiarum Fennica) in its centenary year, 1938.

Biography

Lindelöf studied at the

University of Helsinki The University of Helsinki (, ; UH) is a public university in Helsinki, Finland. The university was founded in Turku in 1640 as the Royal Academy of Åbo under the Swedish Empire, and moved to Helsinki in 1828 under the sponsorship of Alexander ...

, where he completed his

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

in 1893, became a

docent The term "docent" is derived from the Latin word , which is the third-person plural present active indicative of ('to teach, to lecture'). Becoming a docent is often referred to as habilitation or doctor of science and is an academic qualifi ...

in 1895 and

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

of Mathematics in 1903. He was a member of the

Finnish Society of Sciences and Letters The Finnish Society of Sciences and Letters (, , ) is a Finnish learned society for natural sciences, social sciences and humanities. It is a bilingual (Swedish and Finnish) science academy and the oldest of the four science academies in Finland. ...

. In addition to working in a number of different mathematical domains including

conformal mapping In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\i ...

ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematic ...

s and the

gamma function In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...

, Lindelöf promoted the study of the history of Finnish mathematics. He is known for the

Picard–Lindelöf theorem In mathematics, specifically the study of differential equations, the Picard–Lindelöf theorem gives a set of conditions under which an initial value problem has a unique solution. It is also known as Picard's existence theorem, the Cauchy– ...

on differential equations and the

Phragmén–Lindelöf principle In complex analysis, the Phragmén–Lindelöf principle (or method), first formulated by Lars Edvard Phragmén (1863–1937) and Ernst Leonard Lindelöf (1870–1946) in 1908, is a technique which employs an auxiliary, parameterized function to pr ...

, one of several refinements of the

maximum modulus principle In mathematics, the maximum modulus principle in complex analysis states that if f is a holomorphic function, then the modulus , f, cannot exhibit a strict maximum that is strictly within the domain of f. In other words, either f is locally ...

that he proved in

complex function theory Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic g ...

. He was the PhD supervisor for

Lars Ahlfors Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his textbook on complex analysis. Background Ahlfors was born in Helsinki, Finland. His mothe ...

at the

Selected bibliography

*''Le calcul des résidus et ses applications à la théorie des fonctions (Paris, 1905) *''Mémoire sur la théorie des fonctions entières d'ordre fini ("Acta societatis scientiarum fennicae" 31, 1903)'' *With

Lars Edvard Phragmén Lars Edvard Phragmén (2 September 1863, Örebro – 14 March 1937) was a Swedish mathematician who made contributions to complex analysis, voting theory, and actuarial science. He succeeded Sofia Kovalevskaia as professor of mathematical analys ...

: "Sur une extension d'un principe classique de l'analyse et sur quelques propriétés des fonctions monogènes dans le voisinage d'un point singulier", in: ''

Acta Mathematica ''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...

'' 31, 1908.

References

External links

* * * * 1870 births 1946 deaths Scientists from Helsinki 20th-century Finnish mathematicians Topologists 19th-century Finnish mathematicians Academic staff of the University of Helsinki Members of the Royal Society of Sciences in Uppsala Mathematicians from the Russian Empire {{Europe-mathematician-stub