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Hyper-power series and generalized real analytic functions

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Main Authors: Diksha, Tiwari, Akbarali, Mukhammadiev, Paolo, Giordano
Format: Book
Language:English
Published: Springer 2023
Subjects:
non-Archimedean ring of Colombeau
local uniform upper bounds of derivatives
Online Access:https://link.springer.com/article/10.1007/s00605-023-01849-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7483
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spelling oai:localhost:PNK-74832023-04-04T04:28:08Z Hyper-power series and generalized real analytic functions Diksha, Tiwari Akbarali, Mukhammadiev Paolo, Giordano non-Archimedean ring of Colombeau local uniform upper bounds of derivatives CC BY This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in the non-Archimedean ring of Colombeau generalized numbers in this journal. We study one variable hyper-power series by analyzing the notion of radius of convergence and proving classical results such as algebraic operations, composition and reciprocal of hyper-power series. We then define and study one variable generalized real analytic functions, considering their derivation, integration, a suitable formulation of the identity theorem and the characterization by local uniform upper bounds of derivatives. 2023-04-04T04:28:07Z 2023-04-04T04:28:07Z 2023 Book https://link.springer.com/article/10.1007/s00605-023-01849-8 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7483 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic non-Archimedean ring of Colombeau
local uniform upper bounds of derivatives
spellingShingle non-Archimedean ring of Colombeau
local uniform upper bounds of derivatives
Diksha, Tiwari
Akbarali, Mukhammadiev
Paolo, Giordano
Hyper-power series and generalized real analytic functions
description CC BY
format Book
author Diksha, Tiwari
Akbarali, Mukhammadiev
Paolo, Giordano
author_facet Diksha, Tiwari
Akbarali, Mukhammadiev
Paolo, Giordano
author_sort Diksha, Tiwari
title Hyper-power series and generalized real analytic functions
title_short Hyper-power series and generalized real analytic functions
title_full Hyper-power series and generalized real analytic functions
title_fullStr Hyper-power series and generalized real analytic functions
title_full_unstemmed Hyper-power series and generalized real analytic functions
title_sort hyper-power series and generalized real analytic functions
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00605-023-01849-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7483
_version_ 1762274898755977216
score 8.881002

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