Characterizations of derivations on spaces of smooth functions

Characterizations of derivations on spaces of smooth functions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Characterizations of derivations on spaces of smooth functions Włodzimierz Fechner, Aleksandra Świątczak This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2176052/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Dec, 2022 Read the published version in Aequationes mathematicae → Version 1 posted 7 You are reading this latest preprint version Abstract We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation. Mathematics Subject Classification (2010). Primary: 39B42; Secondary: 39B72, 39B82, 47B47. derivations smooth functions. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 30 Dec, 2022 Read the published version in Aequationes mathematicae → Version 1 posted Editorial decision: Major revision 20 Oct, 2022 Reviews received at journal 20 Oct, 2022 Reviewers agreed at journal 20 Oct, 2022 Reviewers invited by journal 19 Oct, 2022 Editor assigned by journal 19 Oct, 2022 Submission checks completed at journal 18 Oct, 2022 First submitted to journal 17 Oct, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2176052","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":145166200,"identity":"d40e46c9-a523-4ed4-8f86-9cd1c8fa0596","order_by":0,"name":"Włodzimierz Fechner","email":"data:image/png;base64,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","orcid":"","institution":"Lodz University of Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Włodzimierz","middleName":"","lastName":"Fechner","suffix":""},{"id":145166201,"identity":"17cd7e2c-b43b-4422-9b3f-033eaa4466ba","order_by":1,"name":"Aleksandra Świątczak","email":"","orcid":"","institution":"Lodz University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Aleksandra","middleName":"","lastName":"Świątczak","suffix":""}],"badges":[],"createdAt":"2022-10-17 17:29:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2176052/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2176052/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00010-022-00934-x","type":"published","date":"2022-12-30T18:07:25+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":28048147,"identity":"88b9925d-f3cc-4563-8856-406f7db4e928","added_by":"auto","created_at":"2022-10-20 15:48:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":237848,"visible":true,"origin":"","legend":"","description":"","filename":"articlecorrected.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2176052/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Characterizations of derivations on spaces of smooth functions","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-2176052/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"aequationes-mathematicae","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aeqm","sideBox":"Learn more about [Aequationes mathematicae](http://link.springer.com/journal/10)","snPcode":"10","submissionUrl":"https://submission.nature.com/new-submission/10/3","title":"Aequationes mathematicae","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"derivations, smooth functions.","lastPublishedDoi":"10.21203/rs.3.rs-2176052/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2176052/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification (2010). Primary: 39B42; Secondary: 39B72, 39B82, 47B47.\u003c/p\u003e","manuscriptTitle":"Characterizations of derivations on spaces of smooth functions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-20 15:48:25","doi":"10.21203/rs.3.rs-2176052/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2022-10-20T11:15:06+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-10-20T11:01:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"2e8930c2-0f0a-4526-9788-792cb5c10b64","date":"2022-10-20T06:18:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-10-19T20:25:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-10-19T20:19:16+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-10-18T13:00:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"Aequationes mathematicae","date":"2022-10-17T17:17:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"aequationes-mathematicae","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aeqm","sideBox":"Learn more about [Aequationes mathematicae](http://link.springer.com/journal/10)","snPcode":"10","submissionUrl":"https://submission.nature.com/new-submission/10/3","title":"Aequationes mathematicae","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8879ae42-68d3-45b5-bd13-357ea8a3eda1","owner":[],"postedDate":"October 20th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T18:12:41+00:00","versionOfRecord":{"articleIdentity":"rs-2176052","link":"https://doi.org/10.1007/s00010-022-00934-x","journal":{"identity":"aequationes-mathematicae","isVorOnly":false,"title":"Aequationes mathematicae"},"publishedOn":"2022-12-30 18:07:25","publishedOnDateReadable":"December 30th, 2022"},"versionCreatedAt":"2022-10-20 15:48:25","video":"","vorDoi":"10.1007/s00010-022-00934-x","vorDoiUrl":"https://doi.org/10.1007/s00010-022-00934-x","workflowStages":[]},"version":"v1","identity":"rs-2176052","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2176052","identity":"rs-2176052","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}