Pub Date : 2023-11-26DOI: 10.1007/s11117-023-01022-3
J. C. Guella, J. Jäger
We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their expansion in eigenfunctions of the Laplace–Beltrami operator. We also present a characterisation of this kernel class. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.
{"title":"Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: the asymptotic approach","authors":"J. C. Guella, J. Jäger","doi":"10.1007/s11117-023-01022-3","DOIUrl":"https://doi.org/10.1007/s11117-023-01022-3","url":null,"abstract":"<p>We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their expansion in eigenfunctions of the Laplace–Beltrami operator. We also present a characterisation of this kernel class. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"80 ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-09DOI: 10.1007/s11117-023-01019-y
Sameh Bououn
{"title":"The interplay between algebras and lattices: Stone–Weierstrass for illustration","authors":"Sameh Bououn","doi":"10.1007/s11117-023-01019-y","DOIUrl":"https://doi.org/10.1007/s11117-023-01019-y","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":" 42","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1007/s11117-023-01020-5
Raluca Dumitru, Jose A. Franco
{"title":"Near order and metric-like functions on the cone of positive definite matrices","authors":"Raluca Dumitru, Jose A. Franco","doi":"10.1007/s11117-023-01020-5","DOIUrl":"https://doi.org/10.1007/s11117-023-01020-5","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"5 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-05DOI: 10.1007/s11117-023-01018-z
Sakshi Gupta, Rekha Gupta, Manjari Srivastava
{"title":"On scalarization and well-posedness in set optimization with a partial set order relation","authors":"Sakshi Gupta, Rekha Gupta, Manjari Srivastava","doi":"10.1007/s11117-023-01018-z","DOIUrl":"https://doi.org/10.1007/s11117-023-01018-z","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"10 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135725041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-16DOI: 10.1007/s11117-023-01015-2
H. Raubenheimer, J. van Appel
Abstract Let A be a Banach algebra and let $$xin A$$ x∈A have the property that its spectrum does not separate 0 from infinity. It is well known that x has a logarithm, i.e., there exists $$yin A$$ y∈A with $$x=e^y$$ x=ey . We will use this statement to identify measures defined on a locally compact group to have logarithms. Also, we will show that the converse of the above statement is in general not true. Our results will be related to infinitely divisible probability measures.
摘要设A是一个Banach代数，且设$$xin A$$ x∈A具有其谱不将0与无穷分开的性质。众所周知，x有对数，即存在$$yin A$$ y∈a，且$$x=e^y$$ x = ey。我们将使用这个语句来确定在局部紧群上定义的具有对数的测度。同样，我们将证明上述陈述的反面通常是不正确的。我们的结果将与无限可分的概率测度有关。
{"title":"On logarithms of measures","authors":"H. Raubenheimer, J. van Appel","doi":"10.1007/s11117-023-01015-2","DOIUrl":"https://doi.org/10.1007/s11117-023-01015-2","url":null,"abstract":"Abstract Let A be a Banach algebra and let $$xin A$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> have the property that its spectrum does not separate 0 from infinity. It is well known that x has a logarithm, i.e., there exists $$yin A$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>y</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> with $$x=e^y$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:mi>y</mml:mi> </mml:msup> </mml:mrow> </mml:math> . We will use this statement to identify measures defined on a locally compact group to have logarithms. Also, we will show that the converse of the above statement is in general not true. Our results will be related to infinitely divisible probability measures.","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"235 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136078262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-15DOI: 10.1007/s11117-023-01016-1
Indranil Sarkar, Gaurav Singh
{"title":"On the uniqueness of continuous positive solution for a non-linear integral equation whose singularity lies in the reciprocal of the solution","authors":"Indranil Sarkar, Gaurav Singh","doi":"10.1007/s11117-023-01016-1","DOIUrl":"https://doi.org/10.1007/s11117-023-01016-1","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136185844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1007/s11117-023-01013-4
Evgeniya Burtseva, Lech Maligranda
Abstract We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also present two new properties of the central Morrey–Orlicz spaces: nontriviality and inclusion property.
{"title":"A new result on boundedness of the Riesz potential in central Morrey–Orlicz spaces","authors":"Evgeniya Burtseva, Lech Maligranda","doi":"10.1007/s11117-023-01013-4","DOIUrl":"https://doi.org/10.1007/s11117-023-01013-4","url":null,"abstract":"Abstract We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also present two new properties of the central Morrey–Orlicz spaces: nontriviality and inclusion property.","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"246 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136064067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s11117-023-01014-3
Marius-Mihai Birou
Abstract In this note we give representations for the remainder in approximations formulas generated by positive linear operators which preserve some functions including linear functions. We show that in these cases the Peano kernel from the integral representation of the remainder has the same sign on the definition domain. Applications to the iterates of some positive linear operators and quadrature formulas are given.
{"title":"A note on the remainder in the approximation of functions by some positive linear operators","authors":"Marius-Mihai Birou","doi":"10.1007/s11117-023-01014-3","DOIUrl":"https://doi.org/10.1007/s11117-023-01014-3","url":null,"abstract":"Abstract In this note we give representations for the remainder in approximations formulas generated by positive linear operators which preserve some functions including linear functions. We show that in these cases the Peano kernel from the integral representation of the remainder has the same sign on the definition domain. Applications to the iterates of some positive linear operators and quadrature formulas are given.","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-30DOI: 10.1007/s11117-023-01010-7
Yukiko Iwata
{"title":"Almost everywhere convergence of the iterates of a bi-stochastic Markov operator","authors":"Yukiko Iwata","doi":"10.1007/s11117-023-01010-7","DOIUrl":"https://doi.org/10.1007/s11117-023-01010-7","url":null,"abstract":"","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136336648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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