astronomy

Johannes Sjöstrand

Johannes Sjöstrand is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Johannes Sjöstrand rather than just read about it. In short: Johannes Sjöstrand (born 1947) is a Swedish mathematician, specializing in partial differential equations and functional analysis. Sjöstrand received his doctorate in 1972 from Lund University under Lars Hörmander.

Key takeaways

Johannes Sjöstrand belongs to astronomy; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Johannes Sjöstrand to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Johannes Sjöstrand from memory before moving on to harder problems.

Reference excerpt

Johannes Sjöstrand (born 1947) is a Swedish mathematician, specializing in partial differential equations and functional analysis. Sjöstrand received his doctorate in 1972 from Lund University under Lars Hörmander. Sjöstrand taught at the University of Paris XI and he is a professor at the University of Burgundy in Dijon. He is a member of the Royal Swedish Academy of Sciences and, since 2017, a member of the American Academy of Arts and Sciences. His research deals with microlocal analysis. He has investigated, inter alia, the Schrödinger equation of an electron in a magnetic field (with a spectrum of the Hofstadter butterfly), resonances in the semiclassical limit, and quantum tunneling in the semiclassical limit.

Selected publications Operators of principal type with interior boundary conditions. Acta mathematica 130, no. 1 (1973): 1–51. doi:10.1007/BF02392261 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. doi:10.1007/BFb0074195 with Richard Melrose: Singularities of boundary value problems. I, Comm. Pure Appl. Math., vol. 31, 1978, pp. 593–619 doi:10.1002/cpa.3160310504; Singularities of boundary value problems. II, Comm. Pure Appl. Math., vol. 35, 1982, pp. 129–168 doi:10.1002/cpa.3160350202 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, see 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: Multiple wells in the semi-classical limit, Part 1, Communications in PDE, 9, 1984, 337–408 (6 parts altogether, see 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, 1988, Nr. 39, 1989, Nr. 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: Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4, 1991, 729–769 doi:10.1090/S0894-0347-1991-1115789-9 with Alain Grigis: Microlocal analysis for differential operators: an introduction, Cambridge University Press 1994. with Mouez Dimassi: Spectral asymptotics in the semi-classical limit, Cambridge University Press 1999 with Maciej Zworski: Asymptotic distribution of resonances for convex obstacles. Acta Mathematica 183, no. 2 (1999): 191–253. doi:10.1007/BF02392828 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. JSTOR 20160036

References

External links Johannes Sjöstrand, IMB, Université de Bourgogne

Worked examples

Example 1 — a first encounter with Johannes Sjöstrand

Start with the simplest possible case. Write down what Johannes Sjöstrand claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Johannes Sjöstrand before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Johannes Sjöstrand ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Johannes Sjöstrand

In research: Johannes Sjöstrand appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Johannes Sjöstrand in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Johannes Sjöstrand is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, Academic staff of the University of Burgundy, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Johannes Sjöstrand outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Johannes Sjöstrand in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Johannes Sjöstrand means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Johannes Sjöstrand out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Johannes Sjöstrand in simple terms?

Why does Johannes Sjöstrand matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Johannes Sjöstrand?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Johannes Sjöstrand.