mathematics

Mischa Cotlar

Mischa Cotlar 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 Mischa Cotlar rather than just read about it. In short: Mischa Cotlar (1913, Sarny, Russian Empire – January 16, 2007, Buenos Aires, Argentina) was a mathematician who started his scientific career in Uruguay and worked most of his life on it in Argentina and Venezuela. His contributions to mathematics are in the fields of harmonic analysis, ergodic theory and spectral theory.

Key takeaways

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

Reference excerpt

Mischa Cotlar (1913, Sarny, Russian Empire – January 16, 2007, Buenos Aires, Argentina) was a mathematician who started his scientific career in Uruguay and worked most of his life on it in Argentina and Venezuela. His contributions to mathematics are in the fields of harmonic analysis, ergodic theory and spectral theory. He introduced the Cotlar–Stein lemma. He was the author or co-author of over 80 articles in refereed journals. According to Alberto Calderón, Cotlar showed in 1955 "that theorems on singular integrals can be generalized and put in the framework of ergodic theory." According to Krause, Lacey, and Wierdl, Karl E. Petersen in 1983 published an "especially direct proof" of Cotlar's 1955 theorem. In January 1994 in Caracas, an international conference was held in his honor.

Selected publications Aritmética abstracta, Boletín de la Facultad de Ingeniería, Montevideo, Uruguay, 1937 Teoría de anágenos, An. Soc. Ci. Argentina, 127, 1939 Familias normales de funciones no analíticas, An. Soc. Ci. Argentina 129, 1940 Un método para obtener congruencias de números de Bernoulli, Math. Notae 7, 1947 On The Foundation Of The Ergodic Theory, Actas Symposia, UNESCO, 1951 Cotlar, Mischa (July 1954). "On a theorem of Beurling and Kaplansky" (PDF). Pacific Journal of Mathematics. 4 (3): 459–466. doi:10.2140/pjm.1954.4.459. with R. Ricabarra: Cotlar, M.; Ricabarra, R. (1954). "On the Existence of Characters in Topological Groups". American Journal of Mathematics. 76 (2): 375–388. doi:10.2307/2372579. JSTOR 2372579. A combinatorial inequality and its application to L2 spaces, Math. Cuyana, 1, 1955 "Sobre lat Teoria algebraica de la Medida y el Teorema de Hahn-Banach" (PDF). Revista de la Unión Matemática Argentina. 17: 9–24. 1956. with R. Panzone: "Generalized potential operators" (PDF). Revista de la Unión Matemática Argentina. 19: 3–41. 1960. Convolution Operators and Factorization, McGill Analysis Seminar, McGill University, Montreal, 1972 "Moment Theory and Continuity of Hilbert and Poisson Transforms in L2 Spaces by M. Cotlar". Functional Analysis, Holomorphy, and Approximation Theory (1st ed.). CRC Press. 1983. doi:10.1201/9781003072577-4. ISBN 9781003072577. S2CID 236816646. "The Helson-Szegö Theorem in Lp by M. Cotlar and C. Sadosky". In: Harmonic Analysis and Partial Differential Equations: Proceedings of a Conference Held April 4-5, 1988. Contemporary Mathematics, vol. 107. American Mathematical Soc. 1990. pp. 19–37. ISBN 9780821851135. with C. Sadosky: Cotlar, M.; Sadosky, C. (1994). "Nehari and Nevanlinna-Pick Problems and Holomorphic Extensions in the Polydisk in Terms of Restricted BMO". Journal of Functional Analysis. 124: 205–210. doi:10.1006/jfan.1994.1105. with Pedro Alegría: Albgría, Pedro; Cotlar, Mischa (1998). "Generalized Toeplitz Forms and Interpolation Colligations". Mathematische Nachrichten. 190: 5–29. doi:10.1002/mana.19981900102. S2CID 121531260.

References

External links Mischa Cotlar at the Mathematics Genealogy Project Horváth, John (2009), "Encounters with Mischa Cotlar", Notices of the American Mathematical Society, 56 (5): 616–620, ISSN 0002-9920, MR 2509066 Zygmund, A. (2002) [1935], Trigonometric Series. Vol. I, II, Cambridge Mathematical Library (3rd ed.), Cambridge University Press, ISBN 978-0-521-89053-3, MR 1963498 Analysis Center, Faculty of Sciences, Central University of Venezuela Mischa Cotlar: A Biography "Barry Simon | Tales of Our Forefathers". YouTube. Rocky Mountain Mathematical Physics Seminar. November 19, 2020. (section on Mischa Cotlar from 51:04 to 57:57)

Illustrations

Worked examples

Example 1 — a first encounter with Mischa Cotlar

Start with the simplest possible case. Write down what Mischa Cotlar 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 Mischa Cotlar 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 Mischa Cotlar 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 Mischa Cotlar

In research: Mischa Cotlar 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 Mischa Cotlar 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: Mischa Cotlar is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1913 births, 2007 deaths, Argentine Jews, so understanding it makes those chapters shorter.
In everyday life: Look for Mischa Cotlar 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 Mischa Cotlar in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mischa Cotlar 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.
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Frequently asked questions

What is Mischa Cotlar in simple terms?

Why does Mischa Cotlar 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 Mischa Cotlar?

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 Mischa Cotlar.