Robert Horton Cameron

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Robert Horton Cameron
Born1908
Died1989
NationalityAmerican
Known forCameron–Martin theorem
AwardsChauvenet Prize (1944)
Scientific career
Fieldsmathematician

Robert Horton Cameron (1908 – 1989, Minnesota) was an American mathematician, who worked on analysis and probability theory. He is known for the Cameron–Martin theorem.

Cameron received his Ph.D. in 1932 from Cornell University under the direction of W. A. Hurwitz.[1][2] He studied under a National Research Council postdoc at the Institute for Advanced Study in Princeton from 1933 to 1935.[3] Cameron was a faculty member at MIT from 1935 to 1945. He was then a faculty member at the University of Minnesota until his retirement. He spent the academic year 1953–1954 on sabbatical leave at the Institute for Advanced Study.[3] His doctoral students include Monroe D. Donsker. He had a total of 35 Ph.D. students at the University of Minnesota — his first two graduated in 1946 and his last one in 1977. Cameron published a total of 72 papers — his first in 1934 and his last, posthumously, in 1990.[4]

At MIT, he did some work with Norbert Wiener. During the 1940s Cameron and W. T. Martin, who was from 1943 to 1946 the chair of the mathematics department at Syracuse University, engaged in an ambitious program of extending Norbert Wiener's early work on mathematical models of Brownian motion.[5] In 1944, Cameron was awarded the Chauvenet Prize for '"Some Introductory Exercises in the Manipulation of Fourier Transforms", which appeared in National Mathematics Magazine, 1941, vol. 15, pages 331–356.

Selected publications[edit]

  • "Almost periodic transformations". Trans. Amer. Math. Soc. 36 (2): 276–291. 1934. doi:10.1090/s0002-9947-1934-1501742-0. MR 1501742.
  • "Implicit functions of almost periodic functions". Bull. Amer. Math. Soc. 40 (12): 895–904. 1934. doi:10.1090/s0002-9904-1934-05999-8. MR 1562996.
  • with Norbert Wiener: "Convergence properties of analytic functions of Fourier–Stieltjes transforms". Trans. Amer. Math. Soc. 46: 97–109. 1939. doi:10.1090/s0002-9947-1939-0000072-0. MR 0000072.
  • with W. T. Martin: "Transformations of Wiener Integrals under Translations". Annals of Mathematics. 45 (2): 386–396. 1944. doi:10.2307/1969276. JSTOR 1969276. (2nd most cited of all Cameron and Martin's papers)
  • with W. T. Martin: "The Wiener measure of Hilbert neighborhoods in the space of real continuous functions". J. Math. Phys. Mass. Inst. Tech. 23 (4): 195–209. 1944. doi:10.1002/sapm1944231195. MR 0011174.
  • with W. T. Martin: "Transformations of Wiener integrals under a general class of linear transformations". Trans. Amer. Math. Soc. 58: 184–219. 1945. doi:10.1090/s0002-9947-1945-0013240-1. MR 0013240.
  • with W. T. Martin: "Evaluation of various Wiener integrals by use of certain Sturm–Liouville differential equations". Bull. Amer. Math. Soc. 51 (2): 73–90. 1945. doi:10.1090/s0002-9904-1945-08275-5. MR 0011401.
  • with W. T. Martin: "The orthogonal development of non-linear functionals in series of Fourier–Hermite functionals". Annals of Mathematics. 48 (2): 385–392. 1947. doi:10.2307/1969178. JSTOR 1969178. (most cited of all Cameron and Martin's papers)
  • with W. T. Martin: "The behavior of measure and measurability under change of scale in Wiener space". Bull. Amer. Math. Soc. 53 (2): 130–137. 1947. doi:10.1090/s0002-9904-1947-08762-0. MR 0019259.
  • with W. T. Martin: "The transformation of Wiener integrals by nonlinear transformations". Trans. Amer. Math. Soc. 66: 253–283. 1949. doi:10.1090/s0002-9947-1949-0031196-6. MR 0031196.
  • with C. Hatfield, Jr.: "On the summability of certain orthogonal developments of nonlinear functionals". Bull. Amer. Math. Soc. 55 (2): 130–145. 1949. doi:10.1090/s0002-9904-1949-09186-3. MR 0028534.
  • "A "Simpson's rule" for the numerical evaluation of Wiener's integrals in function space". Duke Math. J. 18 (1): 111–130. 1951. doi:10.1215/S0012-7094-51-01810-8. MR 0040589.
  • "The first variation of an indefinite Wiener integral". Proc. Amer. Math. Soc. 2: 914–924. 1951. doi:10.1090/s0002-9939-1951-0045937-x. MR 0045937.
  • with R. E. Fagen: "Nonlinear transformations of Volterra type in Wiener space" (PDF). Trans. Amer. Math. Soc. 75: 552–575. 1953. doi:10.1090/s0002-9947-1953-0059476-x. MR 0059476.
  • "The translation pathology of Wiener space". Duke Math. J. 21 (4): 623–627. 1954. doi:10.1215/s0012-7094-54-02165-1. MR 0065033.
  • "A family of integrals serving to connect the Wiener and Feynman integrals". J. Math. and Phys. 39: 126–140. 1960–1961. MR 0127776.
  • with D. A. Storvick: "A translation theorem for analytic Feynman integrals". Trans. Amer. Math. Soc. 125: 1–6. 1966. doi:10.1090/s0002-9947-1966-0200987-0. MR 0200987.
  • with D. A. Storvick: "Analytic continuation for functions of several complex variables". Trans. Amer. Math. Soc. 125: 7–12. 1966. doi:10.1090/s0002-9947-1966-0203081-8. MR 0203081.
  • with D. A. Storvick: "An L2 analytic Fourier–Feynman transform". Michigan Math. J. 23 (1): 1–30. 1976. doi:10.1307/mmj/1029001617. MR 0404571.
  • with D. A. Storvick: A simple definition of the Feynman integral, with applications (paperback). Providence, Rhode Island: AMS. 1983. ISBN 0821822888. (48 pages)

References[edit]

  1. ^ Robert Horton Cameron at the Mathematics Genealogy Project
  2. ^ Cameron, Robert Horton 1908– (WorldCat Identities) Cameron's thesis Almost periodic transformations was published in 3 different editions from 1932 to 1934. The copy in the U. S. Library of Congress is a 1934 edition. A 1932 edition published by Cornell U. is 170 pages long.
  3. ^ a b Cameron, Robert H., Community of Scholars Profile, IAS
  4. ^ Information provided by Prof. Emeritus David Skoug, U. of Nebraska, Feb. 2013
  5. ^ Kac, Mark (1985). Enigmas of Chance. New York: Harper & Row. p. 113. ISBN 0520059867.