mathematics

Kōsaku Yosida

Kōsaku Yosida is a mathematics 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 Kōsaku Yosida rather than just read about it. In short: Kōsaku Yosida (吉田耕作, Yosida Kōsaku; 7 February 1909, Hiroshima – 20 June 1990) was a Japanese mathematician who worked in the field of functional analysis. He is known for the Hille-Yosida theorem concerning C0-semigroups.

Key takeaways

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

Reference excerpt

Kōsaku Yosida (吉田耕作, Yosida Kōsaku; 7 February 1909, Hiroshima – 20 June 1990) was a Japanese mathematician who worked in the field of functional analysis. He is known for the Hille-Yosida theorem concerning C0-semigroups. Yosida studied mathematics at the University of Tokyo, and held posts at Osaka and Nagoya Universities. In 1955, Yosida returned to the University of Tokyo.

See also Einar Carl Hille Functional analysis

References

Kôsaku Yosida: Functional analysis. Grundlehren der mathematischen Wissenschaften 123, Springer-Verlag, 1971 (3rd ed.), 1974 (4th ed.), 1978 (5th ed.), 1980 (6th ed.)

External links Photo Archived 30 June 2013 at the Wayback Machine Kosaku Yosida / School of Mathematics and Statistics University of St Andrews, Scotland 94. Normed Rings and Spectral Theorems, II. By Kôsaku YOSIDA. Mathematical Inlstitute, Nagoya Imperial University. (Comm. by T.TAKAGMI, M.I.A. Oct.12,1943.) Kōsaku Yosida at the Mathematics Genealogy Project Kosaku Yosida (1909 - 1990) - Biography - MacTutor

Illustrations

Worked examples

Example 1 — a first encounter with Kōsaku Yosida

Start with the simplest possible case. Write down what Kōsaku Yosida claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Kōsaku Yosida 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 Kōsaku Yosida 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 Kōsaku Yosida

In research: Kōsaku Yosida appears in mathematics 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 Kōsaku Yosida 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: Kōsaku Yosida is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1909 births, 1990 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kōsaku Yosida 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 Kōsaku Yosida in 20 minutes

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

Frequently asked questions

What is Kōsaku Yosida in simple terms?

Why does Kōsaku Yosida matter?

Because it connects several mathematics 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 Kōsaku Yosida?

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 Kōsaku Yosida.