On close-to-scalar one-parameter cosine families.
Saved in:
| Title: | On close-to-scalar one-parameter cosine families. |
|---|---|
| Authors: | Bobrowski, Adam1 a.bobrowski@pollub.pl, Chojnacki, Wojciech2,3 w.chojnacki@uksw.edu.pl, Gregosiewicz, Adam1 a.gregosiewicz@pollub.pl |
| Source: | Journal of Mathematical Analysis & Applications. Sep2015, Vol. 429 Issue 1, p383-394. 12p. |
| Subjects: | Cosine function, Secant function, Mathematical analysis, Algebra, Mathematical models |
| Abstract: | It is shown that if two cosine families with values in a normed algebra with unity, both indexed by t running over all real numbers, of which one consists of the multiples of the unity of the algebra by numbers of the form cos a t for some real a , differ in norm by less than 8 / ( 3 3 ) uniformly in t , then these families coincide. For a ≠ 0 , the constant 8 / ( 3 3 ) is optimal and cannot be replaced by any larger number. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 102318640 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: On close-to-scalar one-parameter cosine families. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bobrowski%2C+Adam%22">Bobrowski, Adam</searchLink><relatesTo>1</relatesTo><i> a.bobrowski@pollub.pl</i><br /><searchLink fieldCode="AR" term="%22Chojnacki%2C+Wojciech%22">Chojnacki, Wojciech</searchLink><relatesTo>2,3</relatesTo><i> w.chojnacki@uksw.edu.pl</i><br /><searchLink fieldCode="AR" term="%22Gregosiewicz%2C+Adam%22">Gregosiewicz, Adam</searchLink><relatesTo>1</relatesTo><i> a.gregosiewicz@pollub.pl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Sep2015, Vol. 429 Issue 1, p383-394. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Cosine+function%22">Cosine function</searchLink><br /><searchLink fieldCode="DE" term="%22Secant+function%22">Secant function</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: It is shown that if two cosine families with values in a normed algebra with unity, both indexed by t running over all real numbers, of which one consists of the multiples of the unity of the algebra by numbers of the form cos a t for some real a , differ in norm by less than 8 / ( 3 3 ) uniformly in t , then these families coincide. For a ≠ 0 , the constant 8 / ( 3 3 ) is optimal and cannot be replaced by any larger number. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=102318640 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jmaa.2015.04.012 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 383 Subjects: – SubjectFull: Cosine function Type: general – SubjectFull: Secant function Type: general – SubjectFull: Mathematical analysis Type: general – SubjectFull: Algebra Type: general – SubjectFull: Mathematical models Type: general Titles: – TitleFull: On close-to-scalar one-parameter cosine families. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bobrowski, Adam – PersonEntity: Name: NameFull: Chojnacki, Wojciech – PersonEntity: Name: NameFull: Gregosiewicz, Adam IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 0022247X Numbering: – Type: volume Value: 429 – Type: issue Value: 1 Titles: – TitleFull: Journal of Mathematical Analysis & Applications Type: main |
| ResultId | 1 |
