The Hurwitz Product, p-Adic Topology on ℤ, and Fundamental Solution to Linear Differential Equation in the Ring ℤ[[x]]

Gefter, S. L.; Goncharuk, A. B.

doi:10.1007/s10958-017-3651-6

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Cited by 5 publications

(2 citation statements)

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“…In the article [8] we construct an analogue of the convolution (Hurwitz product) of the Euler series…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation

Gefter¹,

Goncharuk²

2021

Preprint

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Consider the linear differential equation of m-th order with constant coefficients from the valuation ring K of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution of this equation from K [[x]]. Also the fundamental solution from 1x K[[ 1 x ]] of the equation is obtained and it is shown that the convolution of the fundamental solution and a non-homogeneity is a unique solution of the equation.

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“…In the article [8] we construct an analogue of the convolution (Hurwitz product) of the Euler series…”

Section: Introductionmentioning

confidence: 99%

“…Using series (19), one can represent the solution of Equation ( 1) as a convolution, as it is done in [8] for the first-order equation and the case (K,…”

mentioning

confidence: 99%

Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation

Gefter¹,

Goncharuk²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Application of the p-Adic Topology on ℤ to the Problem of Finding Solutions in Integers of an Implicit Linear Difference Equation

2018

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Differential Operators of Infinite Order in the Space of Formal Laurent Series and in the Ring of Power Series with Integer Coefficients

Gefter

2019

J Math Sci

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The Hurwitz Product, p-Adic Topology on ℤ, and Fundamental Solution to Linear Differential Equation in the Ring ℤ[[x]]

Cited by 5 publications

References 3 publications

Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation

Linear Differential Equation with Formal Power Series Non-Homogeneity Over a Ring with a Non-Archimedean Valuation

Application of the p-Adic Topology on ℤ to the Problem of Finding Solutions in Integers of an Implicit Linear Difference Equation

Differential Operators of Infinite Order in the Space of Formal Laurent Series and in the Ring of Power Series with Integer Coefficients

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