Pub Date : 2022-10-01DOI: 10.14321/realanalexch.47.2.1654759107
Riddhi Shah, Alok K. Yadav
{"title":"Errata: Dynamics of Certain Distal Actions on Spheres","authors":"Riddhi Shah, Alok K. Yadav","doi":"10.14321/realanalexch.47.2.1654759107","DOIUrl":"https://doi.org/10.14321/realanalexch.47.2.1654759107","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41967284","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 : 2022-09-24DOI: 10.14321/realanalexch.48.1.1663223339
Z. Buczolich
This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis in Paris. This line of research was initiated by a question of Haight and Weizs"aker concerning almost everywhere convergence properties of series of the form $sum_{n=1}^{{infty}}f(nx)$. A more general, additive version of this problem is the following: Suppose $Lambda$ is a discrete infinite set of nonnegative real numbers. We say that $ {Lambda}$ is of type 1 if the series $s(x)=sum_{lambdainLambda}f(x+lambda)$ satisfies a zero-one law. This means that for any non-negative measurable $f: {{mathbb R}}to [0,+ {infty})$ either the convergence set $C(f, {Lambda})={x: s(x)<+ {infty} }= {{mathbb R}}$ modulo sets of Lebesgue zero, or its complement the divergence set $D(f, {Lambda})={x: s(x)=+ {infty} }= {{mathbb R}}$ modulo sets of measure zero. If $ {Lambda}$ is not of type 1 we say that $ {Lambda}$ is of type 2. The exact characterization of type $1$ and type $2$ sets is still not known. The part of the paper discussing results concerning this question is based on several joint papers written at the beginning with J-P. Kahane and D. Mauldin, later with B. Hanson, B. Maga and G. V'ertesy. Apart from results from the above project we also cover historic background, other related results and open questions.
{"title":"Almost Everywhere Convergence Questions of Series of Translates of Non-Negative Functions","authors":"Z. Buczolich","doi":"10.14321/realanalexch.48.1.1663223339","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1663223339","url":null,"abstract":"This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis in Paris. This line of research was initiated by a question of Haight and Weizs\"aker concerning almost everywhere convergence properties of series of the form $sum_{n=1}^{{infty}}f(nx)$. A more general, additive version of this problem is the following: Suppose $Lambda$ is a discrete infinite set of nonnegative real numbers. We say that $ {Lambda}$ is of type 1 if the series $s(x)=sum_{lambdainLambda}f(x+lambda)$ satisfies a zero-one law. This means that for any non-negative measurable $f: {{mathbb R}}to [0,+ {infty})$ either the convergence set $C(f, {Lambda})={x: s(x)<+ {infty} }= {{mathbb R}}$ modulo sets of Lebesgue zero, or its complement the divergence set $D(f, {Lambda})={x: s(x)=+ {infty} }= {{mathbb R}}$ modulo sets of measure zero. If $ {Lambda}$ is not of type 1 we say that $ {Lambda}$ is of type 2. The exact characterization of type $1$ and type $2$ sets is still not known. The part of the paper discussing results concerning this question is based on several joint papers written at the beginning with J-P. Kahane and D. Mauldin, later with B. Hanson, B. Maga and G. V'ertesy. Apart from results from the above project we also cover historic background, other related results and open questions.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46870939","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 : 2022-06-01DOI: 10.14321/realanalexch.47.1.1613920060
E. S. Coulam, T. H. Steele
{"title":"A Characterization of Attractors for Baire Functions on the Interval","authors":"E. S. Coulam, T. H. Steele","doi":"10.14321/realanalexch.47.1.1613920060","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1613920060","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43836900","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 : 2022-06-01DOI: 10.14321/realanalexch.47.1.1625080320
João Paulos
{"title":"On Reflexivity and Point Spectrum","authors":"João Paulos","doi":"10.14321/realanalexch.47.1.1625080320","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1625080320","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43385773","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 : 2022-06-01DOI: 10.14321/realanalexch.47.1.1602263520
S. Koçak, M. Limoncu
{"title":"Generalized Convexity and Passage from Local to Global via Differential Inequalities","authors":"S. Koçak, M. Limoncu","doi":"10.14321/realanalexch.47.1.1602263520","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1602263520","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48702876","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 : 2022-06-01DOI: 10.14321/realanalexch.47.1.1593058128
R. Camerlo
{"title":"Descriptive set theory, from Cantor to Wadge and beyond","authors":"R. Camerlo","doi":"10.14321/realanalexch.47.1.1593058128","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1593058128","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42789040","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 : 2022-06-01DOI: 10.14321/realanalexch.47.1.1628458590
J. Ferrera, J. Gómez Gil, J. Llorente
{"title":"Second Order Differentiability and related topics in the Takagi Class","authors":"J. Ferrera, J. Gómez Gil, J. Llorente","doi":"10.14321/realanalexch.47.1.1628458590","DOIUrl":"https://doi.org/10.14321/realanalexch.47.1.1628458590","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43509496","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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