Henry O. Pollak

Henry O. Pollak
Born
Henry Otto Pollak

(1927-12-13)December 13, 1927
Vienna, Austria
DiedJuly 8, 2026(2026-07-08) (aged 98)
EducationYale University (BS)
Harvard University (MA, PhD)
OccupationMathematician
Known forContributions to information theory

Henry Otto Pollak (December 13, 1927 – July 8, 2026) was an Austrian-American mathematician who has made significant contributions to operator theory, signal analysis, graph theory, and computational geometry.[1]

Life and career

Born in Vienna, Austria, the only child of a lawyer, Pollak fled the Nazis with his family in 1939, first to England and then in 1940 to the US.[2] He received his BS in Mathematics (1947) from Yale University. While at Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University (along with Murray Gell-Mann and Murray Gerstenhaber) that won the second prize in 1947.[3] He earned an M.A. and Ph.D. (1951) degree in mathematics from Harvard University,[4] the latter on the thesis Some Estimates for Extremal Distance advised by Lars Ahlfors.[5]

Pollak then joined Bell Labs (1951),[4] where he later became director of the Mathematics and Statistics Research Center. He has held teaching positions in the mathematics department at Columbia University.[4]

Pollak died on July 8, 2026, at the age of 98.[6]

Research

In several papers with David Slepian and Henry Landau, Pollak developed the theory of what are now known as the Landau–Pollak–Slepian operators on simultaneously time-limited and band-limited functions in operator theory. This work marked an early form of wavelet-based signal analysis.[7]

With Ronald Graham he is the namesake of the Graham–Pollak theorem in graph theory, a result on partitioning the edges of complete graphs into complete bipartite graphs that they published in the early 1970s.[8]

With Edgar Gilbert he is the namesake of the Gilbert–Pollak conjecture relating Steiner trees to Euclidean minimum spanning trees in computational geometry. After they formulated this problem in 1968, it was believed to be proven by Du and Hwang in the early 1990s, but the proof was later determined to be flawed and the problem remains open.[9]

Awards

Selected publications

  • Slepian, D.; Pollak, H. O. (1961). "Prolate spheroidal wave functions, Fourier analysis and uncertainty. I". The Bell System Technical Journal. 40: 43–63. doi:10.1002/j.1538-7305.1961.tb03976.x. MR 0140732.
  • Landau, H. J.; Pollak, H. O. (1961). "Prolate spheroidal wave functions, Fourier analysis and uncertainty. II". The Bell System Technical Journal. 40: 65–84. doi:10.1002/j.1538-7305.1961.tb03977.x. MR 0140733.
  • Landau, H. J.; Pollak, H. O. (1962), "Prolate spheroidal wave functions, Fourier analysis and uncertainty. III. The dimension of the space of essentially time- and band-limited signals", The Bell System Technical Journal, 41: 1295–1336, doi:10.1002/j.1538-7305.1962.tb03279.x, MR 0147686
  • Gilbert, E. N.; Pollak, H. O. (1968). "Steiner minimal trees". SIAM Journal on Applied Mathematics. 16: 1–29. doi:10.1137/0116001. MR 0223269.
  • Graham, R. L.; Pollak, H. O. (1971). "On the addressing problem for loop switching". The Bell System Technical Journal. 50 (8): 2495–2519. doi:10.1002/j.1538-7305.1971.tb02618.x. MR 0289210.
  • Graham, R. L.; Pollak, H. O. (1972). "On embedding graphs in squashed cubes". Graph theory and applications (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1972; dedicated to the memory of J. W. T. Youngs). Lecture Notes in Mathematics. Vol. 303. pp. 99–110. MR 0332576.

References

  1. 1 2 "Mary P. Dolciani Award: Henry Pollak" (PDF). Mathematical Association of America. Retrieved March 3, 2025.
  2. ↑ Roberts, David (October 5, 1998). "Henry Pollak Interview, Part 1 of 4". R. L. Moore legacy collection. Retrieved March 3, 2025.
  3. ↑ G. W. Mackey (1947). "The William Lowell Putnam Mathematical Competition". The American Mathematical Monthly. 54 (7): 400–3. doi:10.1080/00029890.1947.11990193. JSTOR 2304390.
  4. 1 2 3 4 5 6 7 "Henry Otto Pollak, 1975-1976 MAA President". Mathematical Association of America. Archived from the original on January 26, 2013.
  5. ↑ Henry O. Pollak at the Mathematics Genealogy Project
  6. ↑ "In Memoriam: Henry O. Pollak - National Council of Teachers of Mathematics". www.nctm.org. Retrieved July 15, 2026.
  7. ↑ Wong, M. W. (2002). "The Landau-Pollak-Slepian operator". Wavelet Transforms and Localization Operators. Operator Theory: Advances and Applications. Vol. 36. Basel: Birkhäuser. pp. 113–116. doi:10.1007/978-3-0348-8217-0_20. ISBN 9783034882170.
  8. ↑ Aigner, Martin; Ziegler, Günter M. (2018). Proofs from THE BOOK (6th ed.). Springer. pp. 79–80. doi:10.1007/978-3-662-57265-8. ISBN 978-3-662-57265-8.
  9. ↑ Ivanov, A. O.; Tuzhilin, A. A. (2012). "The Steiner ratio Gilbert-Pollak conjecture is still open". Algorithmica. 62 (1–2): 630–632. doi:10.1007/s00453-011-9508-3. MR 2886059.
  10. ↑ Albers, Donald J.; Thibodeaux, Michael J. (June 1984). "A Conversation with Henry Pollak". The College Mathematics Journal. 15 (3). Informa UK Limited: 194–217. doi:10.2307/2686329. JSTOR 2686329.
  11. ↑ "Earle Raymond Hedrick Lecturers". MacTutor History of Mathematics Archive. University of St Andrews. Retrieved March 3, 2025.
  12. ↑ Henry Otto Pollak, honorary Sc.D. Archived 2010-08-02 at the Wayback Machine announcement
  13. ↑ "Honorary doctorates". Eindhoven University of Technology. Retrieved March 3, 2025.
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