{"title":"用三角多项式逼近Lip(α, p), (p > 1)-类的信号(函数)","authors":"K. Khatri, V. Narayan","doi":"10.2298/pim1818251k","DOIUrl":null,"url":null,"abstract":". Given a function f in the class Lip( α,p ) (0 < α 6 1 ,p > 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the n th terms of either certain Riesz mean or Nörlund mean trans-forms of the Fourier series representation for f . They showed that the degree of approximation is O (( λ ( n )) − α ) and extended two theorems of Leindler (2005) where he had weakened the conditions on { p n } given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"46 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Approximation of signals (functions) of Lip(α, p), (p > 1)-class by trigonometric polynomials\",\"authors\":\"K. Khatri, V. Narayan\",\"doi\":\"10.2298/pim1818251k\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Given a function f in the class Lip( α,p ) (0 < α 6 1 ,p > 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the n th terms of either certain Riesz mean or Nörlund mean trans-forms of the Fourier series representation for f . They showed that the degree of approximation is O (( λ ( n )) − α ) and extended two theorems of Leindler (2005) where he had weakened the conditions on { p n } given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices.\",\"PeriodicalId\":416273,\"journal\":{\"name\":\"Publications De L'institut Mathematique\",\"volume\":\"46 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Publications De L'institut Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/pim1818251k\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/pim1818251k","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximation of signals (functions) of Lip(α, p), (p > 1)-class by trigonometric polynomials
. Given a function f in the class Lip( α,p ) (0 < α 6 1 ,p > 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the n th terms of either certain Riesz mean or Nörlund mean trans-forms of the Fourier series representation for f . They showed that the degree of approximation is O (( λ ( n )) − α ) and extended two theorems of Leindler (2005) where he had weakened the conditions on { p n } given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices.