astronomy

Stefan Bergman

Stefan Bergman 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 Stefan Bergman rather than just read about it. In short: Stefan Bergman (5 May 1895 – 6 June 1977) was a Poland-born American mathematician whose primary work was in complex analysis. He is known for the kernel function he discovered in 1922 at University of Berlin.

Key takeaways

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

Reference excerpt

Stefan Bergman (5 May 1895 – 6 June 1977) was a Poland-born American mathematician whose primary work was in complex analysis. He is known for the kernel function he discovered in 1922 at University of Berlin. This function is now known as the Bergman kernel. Bergman taught for many years at Stanford University.

Biography Born in Częstochowa, Congress Poland, Russian Empire, to a German Jewish family, Bergman received his Ph.D. at University of Berlin in 1921, for a dissertation on Fourier analysis. His advisor, Richard von Mises, had a strong influence on him, lasting for the rest of his career. In 1933, Bergman was forced to leave his post at the Berlin University because he was a Jew. He fled first to Russia, where he stayed until 1939, and then to Paris. In 1939, he emigrated to the United States, where he would remain for the rest of life. He was elected a Fellow of the American Academy of Arts and Sciences in 1951. He was a professor at Stanford University from 1952 until his retirement in 1972. He was an invited speaker at the International Congress of Mathematicians in 1950 in Cambridge, Massachusetts and in 1962 in Stockholm (On meromorphic functions of several complex variables). He died in Palo Alto, California, aged 82.

Bergman Prize The Stefan Bergman Prize in mathematics was initiated by Bergman's wife in her will, in memory of her husband's work. The American Mathematical Society supports the prize and selects the committee of judges. The prize is awarded for:

the theory of the kernel function and its applications in real and complex analysis; or function-theoretic methods in the theory of partial differential equations of elliptic type with a special attention to Bergman's and related operator methods.

Selected publications Bergmann, Stefan (1933), "Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. I", Journal für die reine und angewandte Mathematik (in German), 1933 (169): 1–42, doi:10.1515/crll.1933.169.1, JFM 60.1025.01, S2CID 119758238. Bergmann, Stefan (1934), "Über eine in gewissen Bereichen mit Maximumfläche gültige Integraldarstellung der Funktionen zweier komplexer Variabler: I", Mathematische Zeitschrift (in German), 39: 76–94, doi:10.1007/BF01201345, S2CID 120856598, Zbl 0009.26202. Bergmann, Stefan (1935), "Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. II", Journal für die reine und angewandte Mathematik (in German), 1935 (172): 89–128, doi:10.1515/crll.1935.172.89, JFM 60.1025.01, S2CID 199546391. Bergmann, S. (1935), "Über eine in gewissen Bereichen mit Maximumfläche gültige Integraldarstellung der Funktionen zweier komplexer Variabler: II", Mathematische Zeitschrift (in German), 39: 605–608, doi:10.1007/BF01201376, JFM 61.0372.01, S2CID 186228345 Bergmann, S. (1936), "Über eine Integraldarstellung von Funktionen zweier komplexer Veränderlichen", Recueil Mathématique (Matematicheskii Sbornik), New Series (in German), 1 (43) (6): 851–862, Zbl 0016.17001 Bergmann, Stefan (1947) [1941], Sur les fonctions orthogonales de plusieurs variables complexes avec les applications à la théorie des fonctions analytiques., Mémorial des sciences mathématiques (in French), vol. 106 (2nd ed.), Paris: Gauthier-Villars, p. 61, JFM 67.0299.03, MR 0032776, Zbl 0036.05101. The original edition was published in 1941 by Interscience Publishers. Bergmann, Stefan (1948), Sur la fonction-noyau d'un domaine et ses applications dans la théorie des transformations pseudo-conformes., Mémorial des sciences mathématiques (in French), vol. 108, Paris: Gauthier-Villars, p. 80, MR 0032777, Zbl 0036.05201. The Kernel Function and Conformal Mapping, American Mathematical Society 1950, 2nd edn. 1970 with Menahem Max Schiffer: Kernel Functions and elliptic differential equations in mathematical physics, Academic Press 1953 with John G. Herriot: Application of the method of the kernel function for solving boundary value problems, Numerische Mathematik 3, 1961 Integral operators in the theory of linear partial differential equations, Springer 1961, 2nd edn. 1969

See also Bergman kernel Bergman metric Bergman space Bergman–Weil integral representation

References

External links Author profile in the database zbMATH

Illustrations

Worked examples

Example 1 — a first encounter with Stefan Bergman

Start with the simplest possible case. Write down what Stefan Bergman 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 Stefan Bergman 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 Stefan Bergman 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 Stefan Bergman

In research: Stefan Bergman 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 Stefan Bergman 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: Stefan Bergman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1895 births, 1977 deaths, 20th-century Polish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Stefan Bergman 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 Stefan Bergman in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Stefan Bergman 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 Stefan Bergman out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Stefan Bergman in simple terms?

Why does Stefan Bergman 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 Stefan Bergman?

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 Stefan Bergman.