Mischa Cotlar Explained

thumb|right|250px|Mischa Cotlar in 1964Mischa Cotlar (1913, Sarny, Russian Empire – January 16, 2007, Buenos Aires, Argentina)^[1] 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.^[2]

According to Alberto Calderón, Cotlar showed in 1955 "that theorems on singular integrals can be generalized and put in the framework of ergodic theory."^{[3] [4]} According to Krause, Lacey, and Wierdl, Karl E. Petersen in 1983 published an "especially direct proof"^[5] of Cotlar's 1955 theorem.^[6]

In January 1994 in Caracas, an international conference was held in his honor.^[7]

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
• On a theorem of Beurling and Kaplansky. Pacific Journal of Mathematics. July 1954. 4. 3. 459–466. 10.2140/pjm.1954.4.459. Cotlar. Mischa.
• with R. Ricabarra: 10.2307/2372579. 2372579. On the Existence of Characters in Topological Groups. American Journal of Mathematics. 1954. 76. 2. 375–388. Cotlar. M.. Ricabarra. R..
• 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. Revista de la Unión Matemática Argentina. 17. 1956. 9–24.
• with R. Panzone: 1960. Generalized potential operators. Revista de la Unión Matemática Argentina. 19. 3–41.
• Convolution Operators and Factorization, McGill Analysis Seminar, McGill University, Montreal, 1972
• Book: Moment Theory and Continuity of Hilbert and Poisson Transforms in L² Spaces by M. Cotlar. Functional Analysis, Holomorphy, and Approximation Theory. 1st. 1983. CRC Press. 10.1201/9781003072577-4. 9781003072577. 236816646. https://www.taylorfrancis.com/chapters/edit/10.1201/9781003072577-4/moment-theory-continuity-hilbert-poisson-transforms-l2-spaces-cotlar.
• Book: The Helson-Szegö Theorem in L^p by M. Cotlar and C. Sadosky. In: Harmonic Analysis and Partial Differential Equations: Proceedings of a Conference Held April 4-5, 1988. 19–37. Contemporary Mathematics, vol. 107. American Mathematical Soc.. 1990. 9780821851135. https://books.google.com/books?id=YxQcCAAAQBAJ.
• with C. Sadosky: 10.1006/jfan.1994.1105. Nehari and Nevanlinna-Pick Problems and Holomorphic Extensions in the Polydisk in Terms of Restricted BMO. 1994. Journal of Functional Analysis. 124. 205–210. Cotlar. M.. Sadosky. C.. free.
• with Pedro Alegría: 10.1002/mana.19981900102. Generalized Toeplitz Forms and Interpolation Colligations. 1998. Mathematische Nachrichten. 190. 5–29. Albgría. Pedro. Cotlar. Mischa. 121531260 .

External links

• • • • Analysis Center, Faculty of Sciences, Central University of Venezuela
• Mischa Cotlar: A Biography
• Web site: Barry Simon Tales of Our Forefathers. November 19, 2020. Rocky Mountain Mathematical Physics Seminar. YouTube. (section on Mischa Cotlar from 51:04 to 57:57)

Notes and References

1. News: Falleció el notable matemático Mischa Cotlar . The notable mathematician Mischa Cotlar died . Spanish . . January 17, 2007 . https://archive.today/20161009171143/http://www.lanacion.com.ar/875902-fallecio-el-notable-matematico-mischa-cotlar . October 9, 2016 . dead .
2. Book: Sadosky, Cora. Introduction of Professor Mischa Cotlar to the National Academy of Exact Sciences of Argentina by Alberto P. Calderón. xix–xx. Analysis and Partial Differential Equations: A Collection of Papers Dedicated to Mischa Cotlar. 1989. CRC Press. 9781482276923. https://books.google.com/books?id=dDFRDwAAQBAJ&pg=PR20.
3. Calderón, Alberto P.. Ergodic theory and translation-invariant operators. Proceedings of the National Academy of Sciences of the United States of America. 59. 2. 1968. 349–353. 10.1073/pnas.59.2.349. 16591604. 224676. 1968PNAS...59..349C. free.
4. Cotlar, M.. A unified theory of Hilbert transforms and ergodic theorems. Rev. Mat. Cuyana. 1. 2. 1955. 105–167.
5. Krause, B.. Lacey, M.. Wierdl, M.. 2016. On convergence of modulated ergodic Hilbert transforms. math.CA. 1610.04968.
6. Petersen, Karl. Another proof of the existence of the ergodic Hilbert transform. Proc. Amer. Math. Soc.. 88. 1983. 1. 39–43. 10.1090/S0002-9939-1983-0691275-2. 691275. free.
7. Book: Marcantognini, S. A. M.. Mendoza, G. A.. Morán, M. D.. Octavio, A.. Urbina, W. O.. Harmonic Analysis and Operator Theory: A Conference in Honor of Mischa Cotlar, January 3-8, 1994, Caracas, Venezuela. 9780821803042. Contemporary Mathematics, vol. 189. 1995. American Mathematical Soc..