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SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS, II 不区分实值函数的理想收敛的空间，ii
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0367
Miroslav Repický
{"title":"SPACES NOT DISTINGUISHING IDEAL CONVERGENCES OF REAL-VALUED FUNCTIONS, II","authors":"Miroslav Repický","doi":"10.14321/REALANALEXCH.46.2.0367","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0367","url":null,"abstract":"In [13] we gave combinatorial characterizations of non(P) of spaces expressing non-distinguishability of some ideal convergences and semi-convergences of sequences of continuous functions. In the present paper we study three of these invariants: non((I,JQN)-space), none((I,≤KJQN)-space), and none(w(I,JQN)-space). We study them in connection with partial orderings of ωω restricted to relations between I-to-one functions and J-to-one functions. In particular we prove that none(w(I,JQN)-space)≤b for every capacitous ideal J on ω. This generalizes the same result of Kwela for ideals J contained in an Fσ-ideal. If J is a capacitous P-ideal, then non((I,JQN)-space)=none((I,≤KJQN)-space)=b for every ideal I⊆J and none(w(I,JQN)-space)=b for every ideal I below J in the Katĕtov partial quasi-ordering of ideals.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45031448","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}
引用次数: 6
AN EXPLICIT CHARACTERIZATION OF THE DOMAIN OF THE INFINITESIMAL GENERATOR OF A SYMMETRIC DIFFUSION SEMIGROUP ON LP OF A COMPLETE POSITIVE SIGMA-FINITE MEASURE SPACE 完全正SIGMA-FINITE测度空间LP上对称扩散半群无穷小生成元域的显式刻画
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0345
Maxim J. GoldbergSeonja Kim
{"title":"AN EXPLICIT CHARACTERIZATION OF THE DOMAIN OF THE INFINITESIMAL GENERATOR OF A SYMMETRIC DIFFUSION SEMIGROUP ON LP OF A COMPLETE POSITIVE SIGMA-FINITE MEASURE SPACE","authors":"Maxim J. Goldberg, Seonja Kim","doi":"10.14321/REALANALEXCH.46.2.0345","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0345","url":null,"abstract":"Let X be a complete positive σ–finite measure space and {At}t≥0 be a symmetric diffusion semigroup of contraction operators on Lp(X). We prove that for 1<p<∞, the domain of the infinitesimal generator of the semigroup is precisely the space ∫01Ash ds:h∈Lp(X). We also establish that for 1<p<∞, the function spaces 2n-1∫02-(n-1)Ash ds|h∈Lp(X) are equal for every n∈ℤ.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47828414","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}
引用次数: 1
LEBESGUE DENSITY AND STATISTICAL CONVERGENCE LEBESGUE密度与统计收敛
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0495
S. Gła̧bMarek Bienias
{"title":"LEBESGUE DENSITY AND STATISTICAL CONVERGENCE","authors":"Marek Bienias, S. Gła̧b","doi":"10.14321/REALANALEXCH.46.2.0495","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0495","url":null,"abstract":"The paper presents a generalization of the density point’s notion to the ideal-convergence framework. For an ideal I⊆P(ℕ) (with Fin⊆I), Lebesgue measurable set A⊆ℝ we introduce a definition of a density point of A with respect to I; we prove that the classical approach fits into this generalization (Theorem 4); we construct a family of Cantorlike sets showing that Lebesgue Density Theorem cannot be maximally improved in this direction (Theorem 8).","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48233914","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}
引用次数: 0
ON REAL UNIVERSALITY IN THE BIRKHOFF SENSE 论伯克霍夫意义上的实在普遍性
IF 0.2
Real Analysis Exchange Pub Date : 2021-11-01 DOI: 10.14321/REALANALEXCH.46.2.0485
David Rodríguez
{"title":"ON REAL UNIVERSALITY IN THE BIRKHOFF SENSE","authors":"David Rodríguez","doi":"10.14321/REALANALEXCH.46.2.0485","DOIUrl":"https://doi.org/10.14321/REALANALEXCH.46.2.0485","url":null,"abstract":"In this paper we present a proof of the following statement: there is a C∞ function f on ℝn such that any other C∞ function on ℝn is the uniform limit, on the compact subsets of ℝn, of translations of f by natural numbers. This is a real version of the well-known Birkhoff’s result on the existence of a function with a similar property in the space of entire functions. Afterwards, we show that the technique used in our proof allows us to create 2ℵ0 linearly independent real C∞ universal functions. We also demonstrate that we may even obtain real analytic universal functions (in the sense of translations) by using Whitney’s Approximation Theorem.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48443021","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}
引用次数: 0
The Partial Derivative of Okamoto's Functions with Respect to the Parameter 冈本函数对参数的偏导数
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-22 DOI: 10.14321/realanalexch.48.1.1638769133
Nathan DalaklisK. KawamuraTobey MathisMichalis Paizanis
{"title":"The Partial Derivative of Okamoto's Functions with Respect to the Parameter","authors":"Nathan Dalaklis, K. Kawamura, Tobey Mathis, Michalis Paizanis","doi":"10.14321/realanalexch.48.1.1638769133","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1638769133","url":null,"abstract":"The differentiability of the one parameter family of Okomoto's functions as functions of $x$ has been analyzed extensively since their introduction in 2005. As an analogue to a similar investigation, in this paper, we consider the partial derivative of Okomoto's functions with respect to the parameter $a$. We place a significant focus on $a = 1/3$ to describe the properties of a nowhere differentiable function $K(x)$ for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension $1$.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44296262","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}
引用次数: 2
The exponential matrix: an explicit formula by an elementary method 指数矩阵:用初等方法得到的显式公式
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0099
O. D. de Oliveira
{"title":"The exponential matrix: an explicit formula by an elementary method","authors":"O. D. de Oliveira","doi":"10.14321/realanalexch.46.1.0099","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0099","url":null,"abstract":"We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of a real square matrix $A$ of order $ntimes n$. The elementary method developed requires neither Jordan canonical form, nor eigenvectors, nor resolution of linear systems of differential equations, nor resolution of linear systems with constant coefficients, nor matrix inversion, nor complex integration, nor functional analysis. The basic tools are power series and the method of partial fraction decomposition. Two examples are given. A proof of one well-known stability result is given.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":"31 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84848513","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}
引用次数: 0
Ideal extensions of Olivier's theorem 奥利维尔定理的理想扩展
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0261
J. TóthLadislav Misík
{"title":"Ideal extensions of Olivier's theorem","authors":"Ladislav Misík, J. Tóth","doi":"10.14321/realanalexch.46.1.0261","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0261","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41529170","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}
引用次数: 2
Strong derivative and the essentially Riemann integral 强导数和本质上的黎曼积分
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0233
I. GarcesImmanuel D. Calunod
{"title":"Strong derivative and the essentially Riemann integral","authors":"Immanuel D. Calunod, I. Garces","doi":"10.14321/realanalexch.46.1.0233","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0233","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47690486","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}
引用次数: 0
Continuous functions in rings generated by a single Darboux function 由单个达布函数生成的环中的连续函数
IF 0.2
Real Analysis Exchange Pub Date : 2021-10-14 DOI: 10.14321/realanalexch.46.1.0083
Paweł Barbarski
{"title":"Continuous functions in rings generated by a single Darboux function","authors":"Paweł Barbarski","doi":"10.14321/realanalexch.46.1.0083","DOIUrl":"https://doi.org/10.14321/realanalexch.46.1.0083","url":null,"abstract":"","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43796622","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}
引用次数: 0
Quantitative Straightening of Distance Spheres 距离球的定量矫直
IF 0.2
Real Analysis Exchange Pub Date : 2021-07-20 DOI: 10.14321/realanalexch.48.1.1626760923
G. DavidD. PinkertonMcKenna Kaczanowski
{"title":"Quantitative Straightening of Distance Spheres","authors":"G. David, McKenna Kaczanowski, D. Pinkerton","doi":"10.14321/realanalexch.48.1.1626760923","DOIUrl":"https://doi.org/10.14321/realanalexch.48.1.1626760923","url":null,"abstract":"We study\"distance spheres\": the set of points lying at constant distance from a fixed arbitrary subset $K$ of $[0,1]^d$. We show that, away from the regions where $K$ is\"too dense\"and a set of small volume, we can decompose $[0,1]^d$ into a finite number of sets on which the distance spheres can be\"straightened\"into subsets of parallel $(d-1)$-dimensional planes by a bi-Lipschitz map. Importantly, the number of sets and the bi-Lipschitz constants are independent of the set $K$.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43262151","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}
引用次数: 0
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