Lars Hörmander

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–

(

February

2013

)

(

)

Lars Hörmander

Hörmander in 1969

Born

Lars Valter Hörmander

24 January 1931

Died

25 November 2012

(aged 81)

Sweden

Alma mater

Known for

Theory of linear

hyperbolic partial

, the

development of

and

as fundamental tools

Awards

(2006)

(1988)

(1962)

Scientific career

Fields

Institutions

(1955)

Doctoral

students

Lars Valter Hörmander

(24 January 1931 – 25 November 2012) was a

who has been called "the foremost contributor to the modern

theory of linear

Hörmander was awarded the

in 1962 and the

in 1988. In 2006 he was awarded the

for his four-volume textbook

Analysis

of Linear Partial Differential Operators

, which is considered a foundational

work on the subject.

Hörmander completed his

in 1955 at

. Hörmander then

worked at

, at

, and at the

. He returned to Lund University as

a professor from 1968 until 1996, when he retired with the title of

Biography

[

]

Education

[

]

Hörmander was born in

, a village in

in southern Sweden where

his father was a teacher. Like his older brothers and sisters before him, he

attended the

(secondary school), in a nearby town to which he

commuted by train, and the

(high school) in

from which he

graduated in 1948.

At the time when he entered the gymnasium, the principal had instituted an

experiment of reducing the period of the education from three to two years,

and the daily activities to three hours. This freedom to work on his own, "

[greater] than the universities offer in Sweden today", suited Hörmander "very

well". He was also positively influenced by his enthusiastic mathematics

teacher, a

who encouraged him to study university-

level mathematics.

After proceeding to receive a

from Lund University in 1950,

Hörmander began his graduate studies under

(who had also been the

advisor for Hörmander's gymnasium teacher). He made his first research

attempts in classical function theory and

, which "did not

amount to much" but were "an excellent preparation for working in the theory

of partial differential equations." He turned to partial differential equations

when Riesz retired and

who worked actively in that area was

appointed professor.

Hörmander took a one-year break for

from 1953 to 1954, but

due to his position in defense research was able to proceed with his studies

even during that time. His

thesis

On the theory of general partial

differential operators

was finished in 1955, inspired by the nearly concurrent

Ph.D. work of Bernard Malgrange and techniques for hyperbolic differential

operators developed by

and

Fields Medal and years in the U.S.

[

]

Hörmander applied for a professorship at

, but temporarily left for the

while the

request was examined. He spent quarters from winter to fall in respective order at the

, the

, and finally at the

. These locations offered "much to learn" in partial differential equations, with the exception of

Chicago of which he however notes the

seminar held by

and

to have strengthened

his familiarity with harmonic analysis.

In the theory of linear differential operators,

"many people have contributed but the deepest and most significant

results are due to Hörmander", according to Hörmander's doctoral advisor, Lars Gårding.

Hörmander won the

in 1962.

Hörmander was given a position as a part-time professor at Stanford in 1963 but was soon thereafter offered a

professorship at the

in Princeton, New Jersey. He first wished not to leave Sweden but

attempts to find a research professorship in Sweden failed and "the opportunity to do research full time in a

mathematically very active environment was hard to resist", so he accepted the offer and resigned from both Stanford

and Stockholm and began at the Institute in the fall of 1964. Within two years of "hard work", he felt that the

environment at the institute was too demanding, and in 1967 decided to return to Lund after one year. He later noted

that his best work at the institute was done during the remaining year.

Later years

[

]

Hörmander mostly remained at

as a professor after 1968 but made several visits to the United States

during the two next decades. He visited the Courant Institute in 1970, and also the Institute for Advanced Study in

1971 and during the academic year, 1977–1978 when a special year in

was held. He also visited

Stanford in 1971, 1977, and 1982, and the

in winter 1990. Hörmander was briefly

director of the

in Stockholm between 1984 and 1986 but only accepted a two-year appointment

as he "suspected that the administrative duties would not agree well" with him, and found that "the hunch was right".

He also served as vice president of the

between 1987 and 1990. Hörmander retired

in Lund in January 1996. In 2006 he was honored with the

from the

He was made a member of the

in 1968. In 1970 he gave a plenary address (Linear

Differential Operators) at the

He received the 1988

"for fundamental work in modern analysis, in particular, the application of

and

to linear partial differential equations".

In 2012 he was selected as a fellow of the

, but died on 25 November 2012,

before the

list of fellows was released.

Important publications

[

]

His book

Linear Partial Differential Operators

, which largely was the cause for his Fields Medal, has been described

as "the first major account of this theory". It was published by

in 1963 as part of the

series. In the U.S., this book is now in the public domain and reprints are available under ISBN 978-1014977045.

Hörmander devoted five years to compiling the four-volume

The Analysis of Linear Partial Differential

Operators

, first published between 1983 and 1985. A follow-up of his

Linear Partial Differential Operators

"illustrate[d] the vast expansion of the subject"

over the past 20 years, and is considered the "standard of the

field".

In addition to these works, he has written a recognised introduction to

based on

his 1964 Stanford lectures, and wrote the entries on

Hörmander, Lars (2012) [1963],

(Softcover reprint of the original 1st ed.),

, Springer-

Verlag, 2009 [1983],

Springer-Verlag, 2004 [1983],

, Springer-Verlag, 2007

[1985],

, Springer-Verlag, 2009

[1985],

(3rd ed.), North Holland, 1990 [1966],

, 2006 [1994],

, Springer-Verlag, 2003 [1987],