Some results for conjugate equations

[1806.06197] Some results for conjugate equations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Classical Analysis and ODEs arXiv:1806.06197 (math) [Submitted on 16 Jun 2018 ( v1 ), last revised 17 Dec 2018 (this version, v2)] Title: Some results for conjugate equations Authors: Kazuki Okamura View a PDF of the paper titled Some results for conjugate equations, by Kazuki Okamura View PDF HTML (experimental) Abstract: In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider regularity of solutions. In our framework, two iterated function systems are associated with a series of conjugate equations. We state local regularity by using the invariant measures of the two iterated function systems with a common probability vector. We give several examples, especially an example such that infinitely many solutions exists, and a new class of fractal functions on the two-dimensional standard Sierpinski gasket which are not harmonic functions or fractal interpolation functions. We also consider a certain kind of stability. Comments: 28 pages; to appear in Aequationes mathematicae Subjects: Classical Analysis and ODEs (math.CA) ; Dynamical Systems (math.DS) MSC classes: 39B72, 39B12, 28A80, 26A30 Cite as: arXiv:1806.06197 [math.CA] (or arXiv:1806.06197v2 [math.CA] for this version) https://doi.org/10.48550/arXiv.1806.06197 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Aequationes mathematicae 93, No. 6, 1051-1084 (2019) Related DOI : https://doi.org/10.1007/s00010-018-0633-9 Focus to learn more DOI(s) linking to related resources Submission history From: Kazuki Okamura [ view email ] [v1] Sat, 16 Jun 2018 07:07:52 UTC (20 KB) [v2] Mon, 17 Dec 2018 01:44:38 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled Some results for conjugate equations, by Kazuki Okamura View PDF HTML (experimental) TeX Source view license Current browse context: math.CA < prev | next > new | recent | 2018-06 Change to browse by: math math.DS References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Conjugated macrocycles: Excitations get random.#239407
• A mathematical approach to quantum field theory#498710
• Rational linear forms of linearizable ordinary differential equations#1156610
• A study of $m$-ary partitions whose conjugates are $q$-ary#986432
• On Linear-Algebraic Notions of Expansion#391879