mathematics

Pavel Korovkin

Pavel Korovkin 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 Pavel Korovkin rather than just read about it. In short: Pavel Petrovich Korovkin (Russian: Павел Петрович Коровкин) (the family name is also transliterated as Korowkin in German sources) (9 July 1913 – 11 August 1985) was a Soviet mathematician whose main fields of research were orthogonal polynomials, approximation theory and potential theory. In 1947 he proved a generalization of Egorov's theorem: from the early 1950s on, his research interests turned to functional ana…

Key takeaways

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

Reference excerpt

Pavel Petrovich Korovkin (Russian: Павел Петрович Коровкин) (the family name is also transliterated as Korowkin in German sources) (9 July 1913 – 11 August 1985) was a Soviet mathematician whose main fields of research were orthogonal polynomials, approximation theory and potential theory. In 1947 he proved a generalization of Egorov's theorem: from the early 1950s on, his research interests turned to functional analysis and he examined the stability of the exterior Dirichlet problem and the convergence and approximation properties of linear positive operators on spaces of continuous functions. The set of terms and Korovkin approximation are named after him.

Life and career Korovkin was born to a poor peasant family. He lost his father early and grew from 1914 to 1920 at an orphanage. In 1930 he graduated high school in Leningrad. As the winner of a mathematics contest he had a right to enter the Leningrad State University without entrance exams. After a year of working at a factory he entered the Faculty of Mathematics and Mechanics. His scientific advisor was V.I. Smirnov. Korovkin earned his doctorate in 1939 with a dissertation on orthogonal polynomials. He then was appointed to Kalinin Pedagogical Institute. At the beginning of Great Patriotic War Korovkin voluntarily enlisted to the Red Army. He started as a cannon platoon chief and till the end of war promoted to artillery regiment chief. He was awarded with Order of the Red Star. In December 1945, he continued his work at the Kalinin Pedagogical Institute, in 1947 with a thesis on convergence of polynomial sequences, and was appointed professor in 1948. At the Moscow Automobile and Road Institute from 1958 to 1970 he headed the department of higher mathematics, then he became head of the Department of Mathematical Analysis at the Kaluga State Pedagogical Institute.

Selected publications Korovkin, P. P. (1947), "Generalization of a theorem of D. F. Egorov", Doklady Akademii Nauk SSSR (in Russian), 58: 1265–1267, MR 0023322, Zbl 0038.03803. Korovkin, P. P. (1959), Линейные операторы и теория приближений (in Russian), Москва: Физматгиз, p. 211, Zbl 0094.10201, translated in English as Linear operators and approximation theory, Russian monographs and texts on advanced mathematics and physics, vol. III, Hindustan Publishing Corporation (India), 1960, MR 0150565.

Notes

References

Worked examples

Example 1 — a first encounter with Pavel Korovkin

Start with the simplest possible case. Write down what Pavel Korovkin 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 Pavel Korovkin 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 Pavel Korovkin 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 Pavel Korovkin

In research: Pavel Korovkin 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 Pavel Korovkin 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: Pavel Korovkin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1913 births, 1985 deaths, Approximation theorists, so understanding it makes those chapters shorter.
In everyday life: Look for Pavel Korovkin 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 Pavel Korovkin in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pavel Korovkin means in your own words.
Compare your version with the excerpt and mark what you missed.
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Frequently asked questions

What is Pavel Korovkin in simple terms?

Why does Pavel Korovkin 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 Pavel Korovkin?

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 Pavel Korovkin.