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Transactions of the American Mathematical Society

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Structure of complex linear differential equations


Author: Margalit Ronen
Journal: Trans. Amer. Math. Soc. 269 (1982), 429-444
MSC: Primary 34C10; Secondary 30C55, 34A20
DOI: https://doi.org/10.1090/S0002-9947-1982-0637700-8
MathSciNet review: 637700
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Abstract: In this paper homogeneous linear differential equations in the complex domain are considered. Relations between (a) properties of the zeros of solutions, (b) factorization of the equation into linear factors, and (c) nonvanishing of corresponding Wronskians are proved.


References [Enhancements On Off] (What's this?)

  • [1] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin and New York, 1971. MR 0460785 (57:778)
  • [2] W. J. Kim, The Schwarzian derivative and multivalence, Pacific J. Math. 31 (1969), 717-724. MR 0252630 (40:5849)
  • [3] M. Lavie, The Schwarzian derivative and disconjugacy of $ n$-th order linear differential equations, Canad. J. Math. 21 (1969), 235-249. MR 0237874 (38:6153)
  • [4] -, Disconjugacy of linear differential equations in the complex domain, Pacific J. Math. 32 (1970), 435-457. MR 0257447 (41:2098)
  • [5] Z. Nehari, The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc. 55 (1949), 545-551. MR 0029999 (10:696e)
  • [6] A. C. Peterson, On the sign of Green's function beyond the interval of disconjugacy, Rocky Mountain J. Math. 3 (1973), 41-51. MR 0326069 (48:4414)
  • [7] G. Pólya, On the mean value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1924), 312-324. MR 1501228

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0637700-8
Keywords: Disconjugacy, disconjugacy at two points, univalent functions
Article copyright: © Copyright 1982 American Mathematical Society

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