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Transactions of the American Mathematical Society

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Potential theory in the geometry of matrices


Author: Josephine Mitchell
Journal: Trans. Amer. Math. Soc. 79 (1955), 401-422
MSC: Primary 31.0X
DOI: https://doi.org/10.1090/S0002-9947-1955-0072242-6
MathSciNet review: 0072242
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  • [1] S. Bergman, The kernel function and conformal mapping, Mathematical Surveys, No. 5, 1950. MR 0038439 (12:402a)
  • [2] -, Functions of extended class in the theory of functions of several complex variables, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 523-547. MR 0025583 (10:30b)
  • [3] S. Bochner, Functions of several complex variables, Princeton mimeographed notes, Princeton, 1936.
  • [4] -, Group invariance of Cauchy's formula in several variables, Ann. of Math. vol. 45 (1944) pp. 686-707. MR 0011131 (6:123i)
  • [5] R. Courant and D. Hilbert, Methoden der mathematischen Physik, vol. 2, Springer, 1937.
  • [6] G. F. D. Duff and D. C. Spencer, Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. vol. 56 (1952) pp. 128-156. MR 0048137 (13:987a)
  • [7] L. K. Hua, On the theory of automorphic functions of a matrix variable, Amer. J. Math. vol. 66 (1944) pp. 470-488. MR 0011133 (6:124b)
  • [8] C. C. Macduffee, The theory of matrices, Ergebnisse der Mathematik und ihrer Grenzgebiete, Chelsea, 1946.
  • [9] J. Mitchell, The kernel function in the geometry of matrices, Duke Math. J. vol. 19 (1952) pp. 575-584. MR 0050690 (14:368b)
  • [10] Z. Nehari, Conformal mapping, McGraw-Hill, 1952. MR 0045823 (13:640h)
  • [11] F. W. Ponting and H. S. A. Potter, The volume of orthogonal and unitary space, Quarterly Journal of Mathematics vol. 19-20 (1948-1949) pp. 146-154. MR 0030929 (11:75b)
  • [12] L. Pontrjagin, Topological groups, Princeton University Press, 1946.
  • [13] C. L. Siegel, Symplectic geometry, Amer. J. Math. vol. 65 (1943) pp. 1-86. MR 0008094 (4:242b)
  • [14] O. Veblen, Invariants of quadratic differential forms, Cambridge Tracts in Mathematics and Mathematical Physics, No. 24, 1952.
  • [15] K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, 1953. MR 0062505 (15:989f)
  • [16] P. R. Garabedian and D. C. Spencer, A complex tensor calculus for Kähler manifolds, Acta Math. vol. 89 (1953) pp. 279-330. MR 0063119 (16:74a)
  • [17] H. E. Rauch, A ``Poisson'' formula and the Hardy-Littlewood theorem for matrix spaces. Preliminary report, Bull. Amer. Math. Soc. Abstract 55-5-250.
  • [18] M. Sugaward, On the theory of harmonic functions in the general Poincaré-space, J.Fac. Sci. Imp. Univ. Tokyo. Sect. I vol. 5 (1944) pp. 1-32. MR 0015272 (7:395f)

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DOI: https://doi.org/10.1090/S0002-9947-1955-0072242-6
Article copyright: © Copyright 1955 American Mathematical Society

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