Mischa 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.
![](http://upload.luquay.com/wikipedia/commons/thumb/b/b1/Mischa_Cotlar.jpg/250px-Mischa_Cotlar.jpg)
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
edit- 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
edit- ^ "Falleció el notable matemático Mischa Cotlar" [The notable mathematician Mischa Cotlar died] (in Spanish). La Nación. January 17, 2007. Archived from the original on October 9, 2016.
- ^ Sadosky, Cora, ed. (1989). "Introduction of Professor Mischa Cotlar to the National Academy of Exact Sciences of Argentina by Alberto P. Calderón". Analysis and Partial Differential Equations: A Collection of Papers Dedicated to Mischa Cotlar. CRC Press. pp. xix–xx. ISBN 9781482276923.
- ^ Calderón, Alberto P. (1968). "Ergodic theory and translation-invariant operators". Proceedings of the National Academy of Sciences of the United States of America. 59 (2): 349–353. Bibcode:1968PNAS...59..349C. doi:10.1073/pnas.59.2.349. PMC 224676. PMID 16591604.
- ^ Cotlar, M. (1955). "A unified theory of Hilbert transforms and ergodic theorems". Rev. Mat. Cuyana. 1 (2): 105–167.
- ^ Krause, B.; Lacey, M.; Wierdl, M. (2016). "On convergence of modulated ergodic Hilbert transforms". arXiv:1610.04968 [math.CA].
- ^ Petersen, Karl (1983). "Another proof of the existence of the ergodic Hilbert transform". Proc. Amer. Math. Soc. 88 (1): 39–43. doi:10.1090/S0002-9939-1983-0691275-2. MR 0691275.
- ^ Marcantognini, S. A. M.; Mendoza, G. A.; Morán, M. D.; Octavio, A.; Urbina, W. O., eds. (1995). Harmonic Analysis and Operator Theory: A Conference in Honor of Mischa Cotlar, January 3-8, 1994, Caracas, Venezuela. Contemporary Mathematics, vol. 189. American Mathematical Soc. ISBN 9780821803042.
External links
edit- 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)