Linear combinations of logarithmic derivatives of entire functions with applications to differential equations.

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Linear combinations of logarithmic derivatives of entire functions with applications to differential equations.

J. Miles and J. Rossi

Source: Pacific J. Math. Volume 174, Number 1 (1996), 195-214.

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Primary Subjects: 30D35

Secondary Subjects: 34A20

Full-text: Open access

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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102365365
Zentralblatt MATH identifier: 0861.30025
Mathematical Reviews number (MathSciNet): MR1398375

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References

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Mathematical Reviews (MathSciNet): MR83k:34009

Zentralblatt MATH: 0484.34001

[2] S. Bank and J. Langley, Oscillation theory of higher order linear differentialequa- tions with entire coefficients. Complex Variables, 16 (1991), 163-175.

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Zentralblatt MATH: 0745.30032

[3] P. Barry, Some theorems related to the cosp theorem, Proc. London Math. Soc. (3), 21 (1970), 344-360.

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Zentralblatt MATH: 0204.42302

[4] M. Cartwright, Integral Functions, Cambridge University Press, 1956.

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[5] D. Drasin and D. Shea, Convolution inequalities, regular variation and exceptional sets, J. Analyse Math., 29 (1976), 232-293.

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[6] W. Fuchs, Proof of a conjecture of G. Polya concerning gap series, 111. J. Math., 7 (1963), 661-667.

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[7] W. Hayman, Meromorphic Functions, Oxford at the Clarendon Press, 1964.

Mathematical Reviews (MathSciNet): MR29:1337

[8] S. Hellerstein, J. Miles, and J. Rossi, On the growth of solutions of f"+gf+hf= 0, Trans. Amer. Math. Soc, 324 (1991), 693-706.

Mathematical Reviews (MathSciNet): MR91h:30047

Zentralblatt MATH: 0719.34011

[9] S. Hellerstein, J. Miles, and J. Rossi, On the growth of solutions of certain linear differential equations, Ann. Acad. Sci. Fenn., 17 (1992), 343-365.

Mathematical Reviews (MathSciNet): MR93m:34004

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[10] J. Langley, Some oscillation theorems for higher order linear differential equations with entire coefficients of small growth, Results in Math., 20 (1991), 517-529.

Mathematical Reviews (MathSciNet): MR92g:34004

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[11] J. Rossi, Second order differential equations with transcendental coefficients, Proc. Amer. Math. Soc, 97 (1986), 61-66.

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Zentralblatt MATH: 0596.30047

[12] L.-C. Shen, Solution to a problem of S. Bank regardingthe exponent of convergence of the solutions of a differential equation f" + Af --0, Kexue Tongbao, 30 (1985), 1581-1585.

Mathematical Reviews (MathSciNet): MR87j:34020

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[13] D. Townsend, Comparisons between T(r,f) and the total variation of arg f(re) and log \f(rei)\, J. Math. Anal, and Appl., 128 (1987), 347-361.

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