Zorya Shapiro

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Zorya Yakovlevna Shapiro (Russian: Зоря Яковлевна Шапиро; 7 December 1914 – 4 July 2013) was a Soviet mathematician, educator and translator. She is known for her contributions to representation theory and functional analysis in her collaboration with Israel Gelfand, and the Shapiro-Lobatinski condition in elliptical boundary value problems.

Zorya Shapiro attended the Moscow State University Faculty of Mechanics and Mathematics from where she received her undergraduate and doctoral degrees by 1938.^[1] She was active in the military department of the university, especially in aviation, learning to fly and land aeroplanes.^[2]

She started her teaching career at the Faculty, shortly after Zoya Kishkina (1917–1989) and Natalya Eisenstadt (1912–1985), and very quickly became recognized for her courses in analysis.^[1]

Shapiro married Israel Gelfand in 1942. They had 3 sons, one of whom died in childhood.^[3] Shapiro and Gelfand later divorced.^[4]

In the 1980s, Shapiro lived in the same house as Akiva Yaglom.^[5] In 1991 Shapiro moved to River Forest, Illinois to live with her younger son. She died there on 4 July 2013.

Shapiro published several works on representation theory. A contribution (with Gelfand) in integral geometry was to find inversion formulae for the reconstruction of the value of a function on a manifold in terms of integrals over a family of submanifolds, a result with applicability in non-linear differential equations, tomography, multi-dimensional complex analysis and other domains.^[6] Another work was on the representations of rotation groups of 3-dimensional spaces.^[7]

Shapiro is best known for her elucidation of the conditions for well-defined solutions to the elliptical boundary value problem on Sobolev spaces.^[8]

• "О существовании квазиконформных отображений". Доклады АН СССР. 30 (8). 1941.
• "Об эллиптических системах уравнений с частными производными". Доклады АН СССР. XLVI (4): 146–149. 1945.
• "Первая краевая задача для эллиптической системы дифференциальных уравнений" (PDF). Математический сборник. 28(70) (1): 55–78. 1951.
• "Представления группы вращений трёхмерного пространства и их применения". УМН. 7 (1(47)): 3–117. 1952. (with I.M. Gelfand)
• "Об общих краевых задачах для уравнений эллиптического типа" (PDF). Известия АН СССР. 17 (6): 539–565. 1953.
• "Однородные функции и их приложения" (PDF). Успехи математических наук. 10 (3(65)): 3–70. 1955. (with I.M. Gelfand)
• "Об одном классе обобщённых функций" (PDF). Успехи математических наук. 13 (3(81)): 205–212. 1958.
• "Интегральная геометрия на многообразии k-мерных плоскостей". Доклады АН СССР. 168 (6): 1236–1238. 1966. (with I.M. Gelfand, M.I. Graev)
• "Интегральная геометрия на k-мерных плоскостях" (PDF). Функциональный анализ и его приложения. 1 (1): 15–31. 1967. (with I.M. Gelfand, M.I. Graev)
• "Дифференциальные формы и интегральная геометрия" (PDF). Функциональный анализ и его приложения. 3 (2): 24–40. 1969. (with I.M. Gelfand, M.I. Graev)
• "Интегральная геометрия в проективном пространстве". Функциональный анализ и его приложения. 4 (1): 14–32. 1970. (with I.M. Gelfand, M.I. Graev)
• "Локальная задача интегральной геометрии в пространстве кривых" (PDF). Функциональный анализ и его приложения. 13 (2): 11–31. 1979. (with I.M. Gelfand, S.G. Gindikin)

• Representations of the rotation and Lorentz groups and their applications. Macmillan. 1963. (with I.M. Gelfand, R.A. Minlos)

• Jean Leray (1961). Дифференциальное и интегральное исчисления на комплексном аналитическом многообразии. Moscow: Foreign Literature.

• Stanislaw Ulam (1964). Collection of Mathematical Problems [Нерешённые математические задачи]. Moscow: Nauka.
• Robert Finn (1989). Equilibrium Capillary Surfaces [Равновесные капиллярные поверхности: Математическая теория]. Moscow: Mir.