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Transactions of the American Mathematical Society

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Linear operators in the theory of partial differential equations


Author: Stefan Bergman
Journal: Trans. Amer. Math. Soc. 53 (1943), 130-155
MSC: Primary 36.0X
DOI: https://doi.org/10.1090/S0002-9947-1943-0007555-9
MathSciNet review: 0007555
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  • [1] Stefan Bergman, Anwendung des Schwarzschen Lemmas auf eine Klasse von Funktionen von zwei komplexen Veränderlichen, Jber. Deutschen Math. Verein, vol. 39 (1930) pp. 163-168.
  • [2] -, Sur un lien entre la théorie des équations aux derivées partielles elliptiques et celle des fonctions d'une variable complexe, C. R. Acad. Sci. Paris vol. 205 (1937) pp. 1198-1200 and 1360-1362.
  • [3] -, Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen Rec. Math. (Mat. Sbornik) N.S. vol. 2 (1937) pp. 1169-1198.
  • [4] -, The approximation of functions satisfying a linear partial differential equation, Duke Math. J. vol. 6 (1940) pp. 537-561. MR 0003328 (2:201a)
  • [5] -, Boundary values of functions satisfying a linear partial differential equation of elliptic type, Proc. Nat. Acad. Sci. U.S.A. vol. 26 (1940) pp. 668-671. MR 0003327 (2:200e)
  • [6] -, Ueber eine Integraldarstellung von Funktionen zweier komplexer Veränderlichen, Rec. Math. (Mat. Sbornik) N.S. vol. 1 (1936) pp. 851-862.
  • [7] -, Sur les fonctions orthogonales de plusieurs variables complexes, Interscience Publishers, New York, 1941.
  • [8] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Zeit, vol. 34 (1932) pp. 403-439. MR 1545260
  • [9] D. Hilbert, Grundzüge einer allgemeiner Theorie der linearer Integralgleichungen, Leipzig and Berlin, 1912.
  • [10] N. Nielsen, Handbuch der Theorie der Gammafunktionen, Leipzig, 1906.
  • [11] A. Sommerfeld Randwertaufgaben in der Theorie der partiellen Differentialgleichungen. Enzyklopädie der mathematischen Wissenschaften, vol. II, A, 7c pp. 504-570.
  • [12] J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloquium Publications vol. 20, 1935. MR 0218588 (36:1672b)

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DOI: https://doi.org/10.1090/S0002-9947-1943-0007555-9
Article copyright: © Copyright 1943 American Mathematical Society

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