Pub Date : 2003-02-01DOI: 10.1016/S0021-9045(02)00036-9
M. Carro
{"title":"A multiplier theorem using the Schechter's method of interpolation","authors":"M. Carro","doi":"10.1016/S0021-9045(02)00036-9","DOIUrl":"https://doi.org/10.1016/S0021-9045(02)00036-9","url":null,"abstract":"","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125153476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-02-01DOI: 10.1016/S0021-9045(02)00037-0
M. Baronti, E. Casini, C. Franchetti
{"title":"The retraction constant in some Banach spaces","authors":"M. Baronti, E. Casini, C. Franchetti","doi":"10.1016/S0021-9045(02)00037-0","DOIUrl":"https://doi.org/10.1016/S0021-9045(02)00037-0","url":null,"abstract":"","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126351757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper mainly considers the smooth complex spline approximation of Cauchy-type integral operators over an open arc. First, the smoothness of the operators is investigated, then some properties of complex splines are discussed, and finally the error estimates of the approximation are given.
{"title":"The Complex Spline Approximation of Singular Integral Operators over an Open Arc","authors":"Yonglin Xu","doi":"10.1006/jath.2002.3721","DOIUrl":"https://doi.org/10.1006/jath.2002.3721","url":null,"abstract":"This paper mainly considers the smooth complex spline approximation of Cauchy-type integral operators over an open arc. First, the smoothness of the operators is investigated, then some properties of complex splines are discussed, and finally the error estimates of the approximation are given.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127846192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Venancio Alvarez, D. Pestana, José M. Rodríguez, Elena Romera
In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.
{"title":"Weighted Sobolev Spaces on Curves","authors":"Venancio Alvarez, D. Pestana, José M. Rodríguez, Elena Romera","doi":"10.1006/jath.2002.3709","DOIUrl":"https://doi.org/10.1006/jath.2002.3709","url":null,"abstract":"In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125192027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper the constants of strong unicity of minimal projections onto some two-dimensional subspaces in l∞(4) will be calculated.
本文计算了l∞(4)上二维子空间上最小投影的强唯一性常数。
{"title":"Constants of Strong Unicity of Minimal Projections onto some Two-Dimensional Subspaces of linfin(4)","authors":"O. M. Martinov","doi":"10.1006/jath.2002.3714","DOIUrl":"https://doi.org/10.1006/jath.2002.3714","url":null,"abstract":"In this paper the constants of strong unicity of minimal projections onto some two-dimensional subspaces in l∞(4) will be calculated.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"752 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119545005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove asymptotic formulas for the behavior of approximation quantities of identity operators between symmetric sequence spaces. These formulas extend recent results of Defant, Mastylo, and Michels for identities lpn←Fn with an n-dimensional symmetric normed space Fn with p-concavity conditions on Fn and 1 ≤ p ≤ 2. We consider the general case of identities En←Fn with weak assumptions on the asymptotic behavior of the fundamental sequences of the n-dimensional symmetric spaces En and Fn. We give applications to Lorentz and Orlicz sequence spaces, again considerably generalizing results of Pietsch, Defant, Mastylo, and Michels.
{"title":"Approximation Numbers of Identity Operators between Symmetric Sequence Spaces","authors":"A. Hinrichs","doi":"10.1006/jath.2002.3726","DOIUrl":"https://doi.org/10.1006/jath.2002.3726","url":null,"abstract":"We prove asymptotic formulas for the behavior of approximation quantities of identity operators between symmetric sequence spaces. These formulas extend recent results of Defant, Mastylo, and Michels for identities lpn←Fn with an n-dimensional symmetric normed space Fn with p-concavity conditions on Fn and 1 ≤ p ≤ 2. We consider the general case of identities En←Fn with weak assumptions on the asymptotic behavior of the fundamental sequences of the n-dimensional symmetric spaces En and Fn. We give applications to Lorentz and Orlicz sequence spaces, again considerably generalizing results of Pietsch, Defant, Mastylo, and Michels.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"123 40","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117374403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or -1, then the generalized nearest points to x from G exist. We also give a partial answer (Theorem 3.5) to the open problem put forward by S. Fitzpatrick (1989, Bull. Austral. Math. Soc.39, 233-238).
{"title":"Derivatives of Generalized Distance Functions and Existence of Generalized Nearest Points","authors":"Chong Li, R. Ni","doi":"10.1006/jath.2001.3651","DOIUrl":"https://doi.org/10.1006/jath.2001.3651","url":null,"abstract":"The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or -1, then the generalized nearest points to x from G exist. We also give a partial answer (Theorem 3.5) to the open problem put forward by S. Fitzpatrick (1989, Bull. Austral. Math. Soc.39, 233-238).","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"118037233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Necessary and sufficient conditions for the convergence of vector S-fractions are obtained, generalizing classical results of Stieltjes. A class of unbounded difference operators of high order possessing a set of spectral measures is described.
{"title":"Convergence Conditions for Vector Stieltjes Continued Fractions","authors":"Mirta María Castro Smirnova","doi":"10.1006/jath.2001.3653","DOIUrl":"https://doi.org/10.1006/jath.2001.3653","url":null,"abstract":"Necessary and sufficient conditions for the convergence of vector S-fractions are obtained, generalizing classical results of Stieltjes. A class of unbounded difference operators of high order possessing a set of spectral measures is described.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119012034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce operators of q-fractional integration through inverses of the Askey-Wilson operator and use them to introduce a q-fractional calculus. We establish the semigroup property for fractional integrals and fractional derivatives. We study properties of the kernel of q-fractional integral and show how they give rise to a q-analogue of Bernoulli polynomials, which are now polynomials of two variables, x and y. As q->1 the polynomials become polynomials in x-y, a convolution kernel in one variable. We also evaluate explicitly a related kernel of a right inverse of the Askey-Wilson operator on an L^2 space weighted by the weight function of the Askey-Wilson polynomials.
{"title":"Inverse Operators, q-Fractional Integrals, and q-Bernoulli Polynomials","authors":"M. Ismail, Mizan Rahman","doi":"10.1006/jath.2001.3644","DOIUrl":"https://doi.org/10.1006/jath.2001.3644","url":null,"abstract":"We introduce operators of q-fractional integration through inverses of the Askey-Wilson operator and use them to introduce a q-fractional calculus. We establish the semigroup property for fractional integrals and fractional derivatives. We study properties of the kernel of q-fractional integral and show how they give rise to a q-analogue of Bernoulli polynomials, which are now polynomials of two variables, x and y. As q->1 the polynomials become polynomials in x-y, a convolution kernel in one variable. We also evaluate explicitly a related kernel of a right inverse of the Askey-Wilson operator on an L^2 space weighted by the weight function of the Askey-Wilson polynomials.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120262349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the existence of a function @f which is holomorphic exactly in the unit disk D and has universal translates with respect to a prescribed closed set [email protected][email protected]?D and satisfies @[email protected]?C^~(@?DE). If Q is a subsequence of N"0 with upper density d(Q)=1 then the function @f can be constructed such that in [email protected] (z)[email protected]?n=0~a"nz^nwitha"[email protected]?Q.
{"title":"Restricted T-Universal Functions","authors":"W. Luh, V. A. Martirosian, J. Müller","doi":"10.1006/jath.2001.3640","DOIUrl":"https://doi.org/10.1006/jath.2001.3640","url":null,"abstract":"We prove the existence of a function @f which is holomorphic exactly in the unit disk D and has universal translates with respect to a prescribed closed set [email protected][email protected]?D and satisfies @[email protected]?C^~(@?DE). If Q is a subsequence of N\"0 with upper density d(Q)=1 then the function @f can be constructed such that in [email protected] (z)[email protected]?n=0~a\"nz^nwitha\"[email protected]?Q.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126881330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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