Johannes Sjöstrand (born 1947) is a Swedish mathematician, specializing in

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s and

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

. Sjöstrand received his doctorate in 1972 from

Lund University Lund University () is a Public university, public research university in Sweden and one of Northern Europe's oldest universities. The university is located in the city of Lund in the Swedish province of Scania. The university was officially foun ...

under Lars Hörmander. Sjöstrand taught at the University of Paris XI and he is a professor at the University of Burgundy in

Dijon Dijon (, ; ; in Burgundian language (Oïl), Burgundian: ''Digion'') is a city in and the Prefectures in France, prefecture of the Côte-d'Or Departments of France, department and of the Bourgogne-Franche-Comté Regions of France, region in eas ...

. He is a member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences () is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting nat ...

and, since 2017, a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

. His research deals with

microlocal analysis In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes genera ...

. He has investigated, ''inter alia'', the Schrödinger equation of an electron in a magnetic field (with a spectrum of the Hofstadter butterfly), Jean Bellissard ''Le papillon de Hofstadter, d'après B. Helffer et J. Sjöstrand'', Séminaire Bourbaki, Nr. 745, 1991/92
Online
resonances in the semiclassical limit, and

quantum tunneling In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

in the semiclassical limit.

Selected publications

*''Operators of principal type with interior boundary conditions.'' Acta mathematica 130, no. 1 (1973): 1–51. *with Anders Melin: "Fourier integral operators with complex-valued phase functions." In Fourier integral operators and partial differential equations, pp. 120–223. Springer, Berlin, Heidelberg, 1975. *with

Richard Melrose Richard Burt Melrose is an Australian mathematician and emeritus professor at the Massachusetts Institute of Technology who works on geometric analysis, partial differential equations, and differential geometry. Education Melrose received in 19 ...

: ''Singularities of boundary value problems. I'', Comm. Pure Appl. Math., vol. 31, 1978, pp. 593–619 ; ''Singularities of boundary value problems. II'', Comm. Pure Appl. Math., vol. 35, 1982, pp. 129–168 *with Melrose: ''A calculus for Fourier Integral Operators in domains with boundary and applications to the oblique dérivative problem'', Comm. in PDE, 2, 1977, pp. 857–935, se
Helffer ''Propagation des singularités pour des problèmes aux limites'', Séminaire Bourbaki, Nr. 525, 1978/79
*with B. Lascar: ''Singularités analytiques microlocales'', Astérisque 95, 1982 *with

Bernard Helffer Bernard Helffer (born 8 January 1949, Paris) is a French mathematician, specializing in partial differential equations, spectral theory, and mathematical physics. He is the son of the pianist Claude Helffer and the musicologist Mireille Helffer. ...

: ''Multiple wells in the semi-classical limit'', Part 1, Communications in PDE, 9, 1984, 337–408 (6 parts altogether, se
Robert Didier ''Analyse semi-classique de l'effet tunnel'', Séminaire Bourbaki 665, 1985/86
*with Helffer
''Résonances en limite semi-classique''
Mémoire SMF, Nr. 24–25, 1986 *with Helffer: ''Analyse semi-classique pour l'équation de Harper : (avec application à l'équation de Schrödinger avec champ magnétique)'', Mémoire SMF
Nr. 34, 1988Nr. 39, 1989Nr. 40, 1990
(Parts 1–3) *''Asymptotique des résonances pour des obstacles'', Séminaire Bourbaki, Nr. 724, 1989/90 *with Helffer and P. Kerdelhué
''Le papillon de Hofstadter revisité''
Mémoire SMF, Nr. 43, 1990 *with

Maciej Zworski Maciej Zworski is a Polish-Canadian mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include microlocal analysis, scattering theory, and partial differential equations. H ...

: ''Complex scaling and the distribution of scattering poles'', J. Amer. Math. Soc. 4, 1991, 729–769 *with Alain Grigis
''Microlocal analysis for differential operators: an introduction''
Cambridge University Press 1994. *with Mouez Dimassi

Cambridge University Press 1999 *with Maciej Zworski: ''Asymptotic distribution of resonances for convex obstacles.'' Acta Mathematica 183, no. 2 (1999): 191–253.
''Microlocal Analysis''
in: Jean-Paul Pier (ed.): Development of mathematics 1950–2000. Birkhäuser, 2000
''Complete asymptotics for correlations of Laplace integrals in the semi-classical limit''
Paris, SMF 2000 *with Carlos E. Kenig and Gunther Uhlmann: "The Calderón problem with partial data." Annals of mathematics (2007): 567–591.

References

External links

Johannes Sjöstrand, IMB, Université de Bourgogne
{{DEFAULTSORT:Sjostrand, Johannes 1947 births Living people Swedish mathematicians Lund University alumni Academic staff of the University of Burgundy Members of the Royal Swedish Academy of Sciences