About: General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In an earlier paper, we studied solutions g to convolution equations of the form a_dg^{d}+a_{d-1}g^{(d-1)}+...+a_1g+a_0=0, where a_0, ..., a_d are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form \sum_{x\in X} f(x) e^{-sx} (s in C^k), where X is an additive subsemigroup of [0,\infty)^k. If X is discrete and a certain solvability criterion is satisfied, we determine solutions by an elementary recursive approach, adapting an idea of Feckan. The solution of the general case leads us to a more comprehensive question: Let X be an additive subsemigroup of a pointed, closed convex cone C in R^k. Can we find a complex Radon measure on X whose Laplace transform satisfies a given polynomial equation whose coefficients are Laplace transforms of such measures? In an earlier paper, we studied solutions g to convolution equations of the form a_dg^{d}+a_{d-1}g^{(d-1)}+...+a_1g+a_0=0, where a_0, ..., a_d are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form \sum_{x\in X} f(x) e^{-sx} (s in C^k), where X is an additive subsemigroup of [0,\infty)^k. If X is discrete and a certain solvability criterion is satisfied, we determine solutions by an elementary recursive approach, adapting an idea of Feckan. The solution of the general case leads us to a more comprehensive question: Let X be an additive subsemigroup of a pointed, closed convex cone C in R^k. Can we find a complex Radon measure on X whose Laplace transform satisfies a given polynomial equation whose coefficients are Laplace transforms of such measures? (en)
Title	General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms (en)
skos:prefLabel	General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms (en)
skos:notation	RIV/67985807:_____/09:00326688!RIV10-AV0-67985807
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/07/0191), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Porubský, Štefan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	316063
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/09:00326688
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	arithmetic function; Dirichlet convolution; polynomial equation; analytic equation; topological algebra; holomorphic functional calculus; implicit function theorem; Laplace transform; semigroup; complex measure (en)
http://linked.open.../riv/klicoveSlovo	Dirichlet convolution analytic equation complex measure holomorphic functional calculus implicit function theorem polynomial equation topological algebra semigroup Laplace transform arithmetic function
http://linked.open...odStatuVydavatele	PL - Polská republika
http://linked.open...ontrolniKodProRIV	[46862B6B03ED]
http://linked.open...i/riv/nazevZdroje	Studia mathematica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Algebraic, analytic and combinatorial number theory
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	193
http://linked.open...iv/tvurceVysledku	Porubský, Štefan Glöckner, H. Lucht, L. G.
http://linked.open...ain/vavai/riv/wos	000271387800002
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	0039-3223
number of pages	21 (xsd:int)

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