On generalized convolution rengs of arithmetic functions
نویسندگان
چکیده
منابع مشابه
On an Arithmetic Convolution
The Cauchy-type product of two arithmetic functions f and g on nonnegative integers is defined by (f • g)(k) := ∑k m=0 ( k m ) f(m)g(k −m). We explore some algebraic properties of the aforementioned convolution, which is a fundamental characteristic of the identities involving the Bernoulli numbers, the Bernoulli polynomials, the power sums, the sums of products, and so forth.
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Inspired by Rearick (1968), we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials. The EXP is the inverse of LOG. In particular, LOG takes a convolution product of generalized Fibonacci polynomials to a sum of generalized Lucas polynomials and EXP takes the sum to the convolution product. We use this structure to ...
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Arithmetic Convolution Rings
Arithmetic convolution rings provide a general and unified treatment of many rings that have been called arithmetic; the best known examples are rings of complex valued functions with domain in the set of non-negative integers and multiplication the Cauchy product or the Dirichlet product. The emphasis here is on factorization and related properties of such rings which necessitates prior result...
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The purpose of the present paper is to investigate some interesting properties on generalized convolutions of functions for the classes HP ∗(α),HS(α) andHC(α). Further, an application of the convolution on certain integral operator are mentioned. AMS 2010 Mathematics Subject Classification : 30C45, 26D15.
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1980
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496159171