In this paper we characterize subsequences of Fejer means with respect to Vilenkin systems, which are bounded from the Hardy space $H_{p}$ to the Lebesgue space $L_{p},$ for all $0
本文刻画了从Hardy空间$H_{p}$到Lebesgue空间$L_{p} $对所有$0
{"title":"On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces","authors":"L. Persson, G. Tephnadze, G. Tutberidze","doi":"10.7153/oam-2020-14-22","DOIUrl":"https://doi.org/10.7153/oam-2020-14-22","url":null,"abstract":"In this paper we characterize subsequences of Fejer means with respect to Vilenkin systems, which are bounded from the Hardy space $H_{p}$ to the Lebesgue space $L_{p},$ for all $0<p<1/2.$ The result is in a sense sharp.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"109 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78084424","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 : 2020-01-21DOI: 10.1007/978-3-030-60622-0_5
D. Marian, Sorina Anamaria Ciplea, N. Lungu, T. Rassias
{"title":"Hyers–Ulam Stability for Differential Equations and Partial Differential Equations via Gronwall Lemma","authors":"D. Marian, Sorina Anamaria Ciplea, N. Lungu, T. Rassias","doi":"10.1007/978-3-030-60622-0_5","DOIUrl":"https://doi.org/10.1007/978-3-030-60622-0_5","url":null,"abstract":"","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90649202","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 : 2020-01-20DOI: 10.21136/MB.2021.0014-20
P. Rocha
We study Lp-improving properties as well as the type set of certain singular measures on the Heisenberg group.
我们研究了Heisenberg群上某些奇异测度的改进lp性质和类型集。
{"title":"$L^p$-improving properties of certain singular measures on the Heisenberg group","authors":"P. Rocha","doi":"10.21136/MB.2021.0014-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0014-20","url":null,"abstract":"We study Lp-improving properties as well as the type set of certain singular measures on the Heisenberg group.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88533051","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 : 2020-01-12DOI: 10.1215/00192082-8622664
Philippe Jaming, Michael Speckbacher
In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1
在本文中，我们证明函数的展开式 $L^p$-佩利-维纳型空间的长球面波函数几乎处处收敛 $1
{"title":"Almost everywhere convergence of prolate spheroidal series","authors":"Philippe Jaming, Michael Speckbacher","doi":"10.1215/00192082-8622664","DOIUrl":"https://doi.org/10.1215/00192082-8622664","url":null,"abstract":"In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<infty$, even in the cases when they might not converge in $L^p$-norm. We thereby consider the classical Paley-Wiener spaces $PW_c^psubset L^p(mathcal{R})$ of functions whose Fourier transform is supported in $[-c,c]$ and Paley-Wiener like spaces $B_{alpha,c}^psubset L^p(0,infty)$ of functions whose Hankel transform $mathcal{H}^alpha$ is supported in $[0,c]$.As a side product, we show the continuity of the projection operator $P_c^alpha f:=mathcal{H}^alpha(chi_{[0,c]}cdot mathcal{H}^alpha f)$ from $L^p(0,infty)$ to $L^q(0,infty)$, $1<pleq q<infty$.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89199713","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}
Identities and inequalities for the cosine and sine functions are obtained. 1. STATEMENTS AND DISCUSSION The basic result of this note is Theorem 1.1. For any real x (1.1) cosπx = ∞ ∑ j=1 t jπ j(1/4− x2) j,
得到了余弦函数和正弦函数的恒等式和不等式。1. 陈述与讨论本笔记的基本结果是定理1.1。对于任意实数x (1.1) cosπx =∞∑j=1 t jπ j(1/4−x2) j，
{"title":"Identities and inequalities for the cosine and sine functions","authors":"I. Pinelis","doi":"10.7153/mia-2020-23-62","DOIUrl":"https://doi.org/10.7153/mia-2020-23-62","url":null,"abstract":"Identities and inequalities for the cosine and sine functions are obtained. 1. STATEMENTS AND DISCUSSION The basic result of this note is Theorem 1.1. For any real x (1.1) cosπx = ∞ ∑ j=1 t jπ j(1/4− x2) j,","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74298104","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}
A Hurwitz stable polynomial of degree $ngeq1$ has a Hadamard factorization if it is a Hadamard product (i.e. element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. We show that for arbitrary $ngeq4$ there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.
{"title":"On the Existence of Hurwitz Polynomials with no Hadamard Factorization","authors":"S. Bialas, Michal G'ora","doi":"10.13001/ela.2020.5097","DOIUrl":"https://doi.org/10.13001/ela.2020.5097","url":null,"abstract":"A Hurwitz stable polynomial of degree $ngeq1$ has a Hadamard factorization if it is a Hadamard product (i.e. element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. We show that for arbitrary $ngeq4$ there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89827128","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 construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).
{"title":"On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: A constructive approach","authors":"Frederik Broucke, Gregory Debruyne, J. Vindas","doi":"10.1090/proc/15320","DOIUrl":"https://doi.org/10.1090/proc/15320","url":null,"abstract":"We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80136204","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 : 2020-01-01DOI: 10.1007/978-3-030-36020-7_8
J. Bourgain, Mariusz Mirek, E. Stein, B. Wróbel
{"title":"On Discrete Hardy–Littlewood Maximal Functions over the Balls in $${boldsymbol {mathbb {Z}^d}}$$ : Dimension-Free Estimates","authors":"J. Bourgain, Mariusz Mirek, E. Stein, B. Wróbel","doi":"10.1007/978-3-030-36020-7_8","DOIUrl":"https://doi.org/10.1007/978-3-030-36020-7_8","url":null,"abstract":"","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"46 1","pages":"127-169"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77070045","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 : 2019-12-30DOI: 10.1007/978-3-030-42400-8_6
V. Spiridonov
{"title":"Introduction to the Theory of Elliptic Hypergeometric Integrals","authors":"V. Spiridonov","doi":"10.1007/978-3-030-42400-8_6","DOIUrl":"https://doi.org/10.1007/978-3-030-42400-8_6","url":null,"abstract":"","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"18 1","pages":"271-318"},"PeriodicalIF":0.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74435658","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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