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Helmut H. Schaefer

Helmut H. Schaefer 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 Helmut H. Schaefer rather than just read about it. In short: Helmut Heinrich Schaefer (February 14, 1925 in Großenhain, Weimar Republic – December 16, 2005 in Tübingen, Germany) was a German mathematician, who worked primarily in functional analysis. His two best known scientific monographs are titled Topological Vector Spaces (1966) and Banach Lattices and Positive Operators (1974).

Helmut H. Schaefer — main illustration
Helmut H. Schaefer — illustration

Key takeaways

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

Reference excerpt

Helmut Heinrich Schaefer (February 14, 1925 in Großenhain, Weimar Republic – December 16, 2005 in Tübingen, Germany) was a German mathematician, who worked primarily in functional analysis. His two best known scientific monographs are titled Topological Vector Spaces (1966) and Banach Lattices and Positive Operators (1974). The first of these was subsequently translated into Spanish and Russian. The second made him an internationally recognized and leading scholar in this particular field of mathematics. (Roquette & Wolff, 2006)

Education and career As teenager, Helmut Schaefer attended the Sankt Afra boarding school for gifted children in Meissen, Germany on a merit-based scholarship. In 1943, then 18, he was recruited to serve as interpreter of Anglo-American intelligence. After the war he studied mathematics at TU Dresden and University of Leipzig, where he earned his doctorate in 1951 and his habilitation in 1954. Prof. Ernst Hölder served as his academic advisor in Leipzig. In 1956 he accepted an offer from the University of Halle as professor of mathematics. In 1957, Schaefer, his wife and two children escaped from East Germany to the Federal Republic. For one year, he worked under Prof. Gottfried Köthe at the University of Mainz. In 1958 he became associate professor at Washington State University at Pullman and a few years later he, his wife and now three children moved on to the University of Michigan at Ann Arbor. Then in 1963 he accepted an offer from the University of Tübingen in Germany where he remained until his retirement in 1990. In Tübingen he served two terms as department head. Interrupting this period on several occasions and following retirement in Tübingen he spent a number of one-year terms or semesters as visiting or full professor at various American universities, including the University of Illinois Urbana-Champaign, the University of Maryland at College Park, the California Institute of Technology in Pasadena, Texas A&M University at College Station, and Florida Atlantic University at Boca Raton. He remained active in mathematical research until the year 1999, at which point he completely dedicated himself to his lifelong hobby of astronomy, especially astrophotography. In 1978, Helmut Schaefer was accepted as full member of the Mathematics and Natural Sciences Class of the Heidelberg Academy of Sciences. Earlier, he was admitted to the Academy of Sciences in Zaragoza (Spain). Over the years, he was able to attract many students to functional analysis, combining an expectation of high achievement with a tolerant, humorous, and factual attitude. Ten of his doctoral students went on to become professors at various universities in Germany and the U.S. (Roquette & Wolff, 2006) His doctoral students include Wolfgang Arendt, Rainer Nagel, and Bertram John Walsh.

Textbooks Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.

References

Peter Roquette and Manfred Wolff (2006), Helmut Schaefer 1925 – 2005, Obituary, Jahrbuch 2005 der Heidelberger Akademie der Wissenschaften Monographs by Helmut H. Schaefer as catalogued by the German National Library Helmut H. Schaefer at the Mathematics Genealogy Project Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.

Illustrations

Helmut H. Schaefer illustration

Worked examples

Example 1 — a first encounter with Helmut H. Schaefer

Start with the simplest possible case. Write down what Helmut H. Schaefer 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 Helmut H. Schaefer 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 Helmut H. Schaefer 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 Helmut H. Schaefer

In research
Helmut H. Schaefer 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 Helmut H. Schaefer 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
Helmut H. Schaefer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 births, 2005 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Helmut H. Schaefer 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 Helmut H. Schaefer in 20 minutes

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

Frequently asked questions

What is Helmut H. Schaefer in simple terms?

Helmut Heinrich Schaefer (February 14, 1925 in Großenhain, Weimar Republic – December 16, 2005 in Tübingen, Germany) was a German mathematician, who worked primarily in functional analysis. His two best known scientific monographs are titled Topological Vector Spaces (1966) and Banach Lattices and…

Why does Helmut H. Schaefer 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 Helmut H. Schaefer?

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 Helmut H. Schaefer.

Tags

  • 1925 births
  • 2005 deaths
  • 20th-century German mathematicians
  • Academic staff of the University of Halle
  • Academic staff of the University of Tübingen
  • Functional analysts
  • German mathematicians
  • Leipzig University alumni
  • People from Großenhain
  • TU Dresden alumni
  • University of Michigan faculty
  • Washington State University faculty

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