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Mischa Cotlar

{{Short description|Argentine mathematician}}

file:Mischa Cotlar.jpg

Mischa Cotlar (1913, Sarny, Russian Empire – January 16, 2007, Buenos Aires, Argentina){{cite news|title=Falleció el notable matemático Mischa Cotlar |trans-title=The notable mathematician Mischa Cotlar died |language=Spanish |publisher=La Nación |url=http://www.lanacion.com.ar/875902-fallecio-el-notable-matematico-mischa-cotlar |date=January 17, 2007 |archive-url=https://archive.today/20161009171143/http://www.lanacion.com.ar/875902-fallecio-el-notable-matematico-mischa-cotlar |archive-date=October 9, 2016 |url-status=dead }} 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.{{cite book|editor=Sadosky, Cora|chapter=Introduction of Professor Mischa Cotlar to the National Academy of Exact Sciences of Argentina by Alberto P. Calderón|pages=xix–xx|title=Analysis and Partial Differential Equations: A Collection of Papers Dedicated to Mischa Cotlar|year=1989|publisher=CRC Press|isbn=9781482276923|chapter-url=https://books.google.com/books?id=dDFRDwAAQBAJ&pg=PR20}}

According to Alberto Calderón, Cotlar showed in 1955 "that theorems on singular integrals can be generalized and put in the framework of ergodic theory."{{cite journal|author=Calderón, Alberto P.|title=Ergodic theory and translation-invariant operators|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=59|issue=2|year=1968|pages=349–353|doi=10.1073/pnas.59.2.349|pmid=16591604|pmc=224676|bibcode=1968PNAS...59..349C|doi-access=free}}{{cite journal|author=Cotlar, M.|title=A unified theory of Hilbert transforms and ergodic theorems|journal=Rev. Mat. Cuyana|volume=1|issue=2|year=1955|pages=105–167}} According to Krause, Lacey, and Wierdl, Karl E. Petersen in 1983 published an "especially direct proof"{{cite arXiv|author=Krause, B.|author2=Lacey, M.|author3=Wierdl, M.|year=2016|title=On convergence of modulated ergodic Hilbert transforms|class=math.CA|eprint=1610.04968}} of Cotlar's 1955 theorem.{{cite journal|author=Petersen, Karl|title=Another proof of the existence of the ergodic Hilbert transform|journal=Proc. Amer. Math. Soc.|volume=88|year=1983|issue=1|pages=39–43|doi=10.1090/S0002-9939-1983-0691275-2|mr=691275|url=https://www.ams.org/journals/proc/1983-088-01/S0002-9939-1983-0691275-2/|doi-access=free}}

In January 1994 in Caracas, an international conference was held in his honor.{{cite book|editor=Marcantognini, S. A. M.|editor2=Mendoza, G. A.|editor3=Morán, M. D.|editor4=Octavio, A.|editor5=Urbina, W. O.|url=https://books.google.com/books?id=H8kaCAAAQBAJ|isbn = 9780821803042|title = Harmonic Analysis and Operator Theory: A Conference in Honor of Mischa Cotlar, January 3-8, 1994, Caracas, Venezuela|series=Contemporary Mathematics, vol. 189|year = 1995|publisher = American Mathematical Soc.}}

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
  • {{cite journal|title=On a theorem of Beurling and Kaplansky|journal=Pacific Journal of Mathematics|date=July 1954|volume=4|issue=3|pages=459–466|doi=10.2140/pjm.1954.4.459|url=https://msp.org/pjm/1954/4-3/pjm-v4-n3-s.pdf#page=141|last1=Cotlar|first1=Mischa}}
  • with R. Ricabarra: {{cite journal|doi=10.2307/2372579|jstor=2372579|title=On the Existence of Characters in Topological Groups|journal=American Journal of Mathematics|year=1954|volume=76|issue=2|pages=375–388|last1=Cotlar|first1=M.|last2=Ricabarra|first2=R.}}
  • A combinatorial inequality and its application to L2 spaces, Math. Cuyana, 1, 1955
  • {{cite journal|title=Sobre lat Teoria algebraica de la Medida y el Teorema de Hahn-Banach|journal=Revista de la Unión Matemática Argentina|volume=17|year=1956|pages=9–24|url=https://inmabb.criba.edu.ar/revuma/pdf/v17/p009-024.pdf}}
  • with R. Panzone: {{cite journal|year=1960|title=Generalized potential operators|journal=Revista de la Unión Matemática Argentina|volume=19|pages=3–41|url=https://inmabb.criba.edu.ar/revuma/pdf/v19n1/p003-041.pdf}}
  • Convolution Operators and Factorization, McGill Analysis Seminar, McGill University, Montreal, 1972
  • {{cite book|chapter=Moment Theory and Continuity of Hilbert and Poisson Transforms in L2 Spaces by M. Cotlar|title=Functional Analysis, Holomorphy, and Approximation Theory|edition=1st|year=1983|publisher=CRC Press|doi=10.1201/9781003072577-4|isbn=9781003072577|s2cid=236816646|chapter-url=https://www.taylorfrancis.com/chapters/edit/10.1201/9781003072577-4/moment-theory-continuity-hilbert-poisson-transforms-l2-spaces-cotlar}}
  • {{cite book|chapter=The Helson-Szegö Theorem in Lp by M. Cotlar and C. Sadosky|title=In: Harmonic Analysis and Partial Differential Equations: Proceedings of a Conference Held April 4-5, 1988|pages=19–37|series=Contemporary Mathematics, vol. 107|publisher=American Mathematical Soc.|year=1990|isbn=9780821851135|chapter-url=https://books.google.com/books?id=YxQcCAAAQBAJ}}
  • with C. Sadosky: {{cite journal|doi=10.1006/jfan.1994.1105|title=Nehari and Nevanlinna-Pick Problems and Holomorphic Extensions in the Polydisk in Terms of Restricted BMO|year=1994|journal=Journal of Functional Analysis|volume=124|pages=205–210|last1=Cotlar|first1=M.|last2=Sadosky|first2=C.|doi-access=free}}
  • with Pedro Alegría: {{cite journal|doi=10.1002/mana.19981900102|title=Generalized Toeplitz Forms and Interpolation Colligations|year=1998|journal=Mathematische Nachrichten|volume=190|pages=5–29|last1=Albgría|first1=Pedro|last2=Cotlar|first2=Mischa| s2cid=121531260 }}

References

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External links

  • {{MathGenealogy|id= 6433}}
  • {{Citation | last1=Horváth | first1=John | author-link1=John Horvath (mathematician) | title=Encounters with Mischa Cotlar |mr=2509066 | year=2009 | journal=Notices of the American Mathematical Society | issn=0002-9920 | volume=56 | issue=5 | pages=616–620}}
  • {{Citation | last1=Zygmund | first1=A. | author-link=Antoni Zygmund | title=Trigonometric Series. Vol. I, II | origyear=1935 | title-link=Trigonometric Series | publisher=Cambridge University Press | edition=3rd | series=Cambridge Mathematical Library | isbn=978-0-521-89053-3 |mr=1963498 | year=2002}}
  • [http://www.matematica.ciens.ucv.ve/centana/mischa/mischa.htm Analysis Center, Faculty of Sciences, Central University of Venezuela]
  • [http://www.math.unm.edu/conferences/10thAnalysis/resources/cotlar/cotlar_bio.pdf Mischa Cotlar: A Biography]
  • {{cite web|title=Barry Simon {{!}} Tales of Our Forefathers|date=November 19, 2020|publisher=Rocky Mountain Mathematical Physics Seminar|website=YouTube|url=https://www.youtube.com/watch?v=vu1Vf179bh4&t=3064s}} (section on Mischa Cotlar from 51:04 to 57:57)

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Category:Argentine mathematicians

Category:Argentine Jews

Category:2007 deaths

Category:1913 births

Category:Soviet emigrants

Category:Immigrants to Uruguay

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