Logarithmic derivatives of solutions to linear differential equations
نویسندگان
چکیده
منابع مشابه
Logarithmic Derivatives of Solutions to Linear Differential Equations
Given an ordinary differential field K of characteristic zero, it is known that if y and 1/y satisfy linear differential equations with coefficients in K, then y/y is algebraic over K. We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over K that y/y satisfies. Moreover, we provide explicit degree bounds and extend the res...
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In the case of a linear constant coefficient differential equation, & = Ax, where x is a (complex) n-vector and A is a (complex) nXn matrix, it is well known when all solutions are bounded; namely, if all eigenvalues of A are purely imaginary and all elementary divisions of A are simple. This condition is equivalent to the Jordan normal form, / , of A being (Hermitian) skew symmetric. That is i...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07444-1