منابع مشابه
Power-monotone Sequences and Integrability of Trigonometric Series
The theorem proved in this paper is a generalization of some results, concerning integrability of trigonometric series, due to R.P. Boas, L. Leindler, etc. This result can be considered as an example showing the utility of the notion of power-monotone sequences.
متن کاملUniserial modules of generalized power series
Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.
متن کاملOn Integrability of Functions Defined by Trigonometric Series
The goal of the present paper is to generalize two theorems of R.P. Boas Jr. pertaining to L (p > 1) integrability of Fourier series with nonnegative coefficients and weight x . In our improvement the weight x is replaced by a more general one, and the case p = 1 is also yielded. We also generalize an equivalence statement of Boas utilizing power-monotone sequences instead of {n}.
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Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...
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)
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1985
ISSN: 0002-9939
DOI: 10.2307/2044757