Coefficients of differentially algebraic series
نویسندگان
چکیده
منابع مشابه
Constructible Differentially Finite Algebraic Series in Several Variables
We extend the concept of CDF-series to the context of several variables, and show that the series solution of first order differential equations y′ = x(t, y) and functional equation y = x(t, y), with x CDF in two variables, are CDF-series. We also give many effective closure properties for CDF-series in several variables. 1. CDF-series in one variable We present in this paper, new properties an...
متن کاملALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)
We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
متن کاملALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)
We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
متن کاملDifferentially Algebraic Gaps
H-fields are ordered differential fields that capture some basic properties of Hardy fields and fields of transseries. Each H-field is equipped with a convex valuation, and solving first-order linear differential equations in Hfield extensions is strongly affected by the presence of a “gap” in the value group. We construct a real closed H-field that solves every first-order linear differential ...
متن کاملConstruction of Algebraic Wavelet Coefficients
In this paper we discuss a method for construction of algebraic wavelet coefficients, i.e., wavelet coefficients lying in an algebraic extension field of Q: The method relies on a strengthened version of a theorem due to L. FEJÉR and F. RIESZ. As an application, we prove that the Daubechies wavelets have algebraic wavelet coefficients. We show that there exist uncountably many transcendent scal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1990
ISSN: 0263-6115
DOI: 10.1017/s1446788700029955