Formal Gevrey Class of Formal Power Series Solution for Singular First Order Linear Partial Differential Operators
نویسندگان
چکیده
منابع مشابه
Gevrey order of formal power series solutions of inhomogeneous partial differential equations with constant coefficients
In an earlier paper, the first author showed that certain normalized formal solutions of homogeneous linear partial differential equations with constant coefficients are multisummable, with a multisummability type that can be determined from a Newton polygon associated with the PDE. In this article, some of the results obtained there are extended in several directions: First of all, arbitrary f...
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The reason why we consider this type of equation will be explained in the end of this section. As mentioned in Part I, we know that the equation (1.1) has a unique formal power series solution in O[R][[y]]2 for some R > 0. Here we say that a formal power series u(x, y) belongs to O[R][[y]]2 if u(x, y) can be written as u(x, y) = ∑∞ n=0 un(x)y , where all un(x) are holomorphic on {x ∈ C; |x| ≤ R...
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Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2000
ISSN: 0387-3870
DOI: 10.3836/tjm/1255958687