T. Bloom, L. Bos, N. Levenberg, S. Ma‘u, F. Piazzon
We correct the calculation of the Monge-Ampere measure of a certain extremal plurisubharmonic function for the complex Euclidean ball in C^2.
修正了C^2中复欧几里得球的某极值多次谐波函数的蒙日-安培测度的计算。
{"title":"Correction/Addendum to “The extremal function for the complex ball for generalized notions of degree and multivariate polynomial approximation” (Ann. Polon. Math. 123 (2019), 171–195)","authors":"T. Bloom, L. Bos, N. Levenberg, S. Ma‘u, F. Piazzon","doi":"10.4064/ap200505-4-8","DOIUrl":"https://doi.org/10.4064/ap200505-4-8","url":null,"abstract":"We correct the calculation of the Monge-Ampere measure of a certain extremal plurisubharmonic function for the complex Euclidean ball in C^2.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46251817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic varieties, and discuss some of its applications to problems in Number Theory. This is an extended version of a talk at the Jubilee Congress for the 100th anniversary of the Polish Mathematical Society, Krakow, 2019.
{"title":"Hodge theory of $p$-adic varieties: a survey","authors":"Wiesalawa Niziol","doi":"10.4064/ap200516-31-8","DOIUrl":"https://doi.org/10.4064/ap200516-31-8","url":null,"abstract":"$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic varieties, and discuss some of its applications to problems in Number Theory. This is an extended version of a talk at the Jubilee Congress for the 100th anniversary of the Polish Mathematical Society, Krakow, 2019.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48966368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that the cyclic inequality $sumlimits_{i=1}^{i=n}left(frac{x_i}{x_{i+1}}right)^kgeqsumlimits_{i=1}^{i=n}frac{x_i}{x_{sigma(i)}}$ holds for $k$ in a specific range dependant on the permutation $sigma$. We also show that the same is not true for the Sahpiro-type generalizations.
{"title":"On a cyclic inequality with exponents and permutations, and its Shapiro-type analogues","authors":"A. Czarnecki, Gabriel Kici'nski","doi":"10.4064/ap210119-6-9","DOIUrl":"https://doi.org/10.4064/ap210119-6-9","url":null,"abstract":"We prove that the cyclic inequality $sumlimits_{i=1}^{i=n}left(frac{x_i}{x_{i+1}}right)^kgeqsumlimits_{i=1}^{i=n}frac{x_i}{x_{sigma(i)}}$ holds for $k$ in a specific range dependant on the permutation $sigma$. We also show that the same is not true for the Sahpiro-type generalizations.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48878843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C-holomorphic functions defined on algebraic sets and having algebraic graphs can be considered as a complex counterpart of regulous functions introduced recently in real geometry. This note is a part of our study on the subject; we prove herein some effective Nullstellensatze.
{"title":"On the Nullstellensatz for c-holomorphic functions with algebraic graphs","authors":"Adam Bialo.zyt, M. Denkowski, P. Tworzewski","doi":"10.4064/ap200218-11-5","DOIUrl":"https://doi.org/10.4064/ap200218-11-5","url":null,"abstract":"C-holomorphic functions defined on algebraic sets and having algebraic graphs can be considered as a complex counterpart of regulous functions introduced recently in real geometry. This note is a part of our study on the subject; we prove herein some effective Nullstellensatze.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47211325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vector-valued functions via tensor product theory. In this paper we study weighted spaces $mathcal{EV}(Omega)$ of smooth functions on an open subset $Omegasubsetmathbb{R}^{d}$ whose topology is given by a family of weights $mathcal{V}$. We derive sufficient conditions on the weights which make $mathcal{EV}(Omega)$ a nuclear space.
{"title":"On the nuclearity of weighted spaces of smooth functions","authors":"K. Kruse","doi":"10.4064/ap190728-17-11","DOIUrl":"https://doi.org/10.4064/ap190728-17-11","url":null,"abstract":"Nuclearity plays an important role for the Schwartz kernel theorem to hold and in transferring the surjectivity of a linear partial differential operator from scalar-valued to vector-valued functions via tensor product theory. In this paper we study weighted spaces $mathcal{EV}(Omega)$ of smooth functions on an open subset $Omegasubsetmathbb{R}^{d}$ whose topology is given by a family of weights $mathcal{V}$. We derive sufficient conditions on the weights which make $mathcal{EV}(Omega)$ a nuclear space.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"124 1","pages":"173-196"},"PeriodicalIF":0.5,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44601531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study topologizability and power boundedness of weigh-ted composition operators on (certain subspaces of) $mathscr{D}'(X)$ for an open subset $X$ of $mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the weight of the weighted composition operator, while for the latter property necessary and sufficient conditions on the weight and the symbol are presented. Moreover, for an unweighted composition operator a characterization of power boundedness in terms of the symbol is derived for the special case of a bijective symbol.
{"title":"Topologizable and power bounded weighted composition operators on spaces of distributions","authors":"T. Kalmes","doi":"10.4064/AP200211-11-5","DOIUrl":"https://doi.org/10.4064/AP200211-11-5","url":null,"abstract":"We study topologizability and power boundedness of weigh-ted composition operators on (certain subspaces of) $mathscr{D}'(X)$ for an open subset $X$ of $mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the weight of the weighted composition operator, while for the latter property necessary and sufficient conditions on the weight and the symbol are presented. Moreover, for an unweighted composition operator a characterization of power boundedness in terms of the symbol is derived for the special case of a bijective symbol.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46275641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Conservation of module and the product of modules of foliations","authors":"A. Kaźmierczak","doi":"10.4064/ap190101-10-6","DOIUrl":"https://doi.org/10.4064/ap190101-10-6","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"124 1","pages":"161-172"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70578663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let P Z n be the additive subgroup of the real Hilbert space L 2 (0 , 1) consisting of polynomials of order ≤ n with integer coefficients. We may treat P Z n as a lattice in ( n + 1) -dimensional Euclidean space; let λ i ( P Z n ) ( 1 ≤ i ≤ n + 1 ) be the corresponding successive minima. We give rather precise estimates of λ i ( P Z n ) for i (cid:38) 23 n .
． 让Z P n成为《additive subgroup 2》真正的希尔伯特空间L (0, 1) consisting of polynomials of秩序和整数n≤coefficients。我们可以在(n + 1) -次欧几里得空间中解决P - n的问题;让λi Z P (n)(1≤i≤n + 1) be the corresponding successive函数。我们给的很精确的保守λi n P (Z) for一世(cid): 38) 23 n。
{"title":"On the lattice of polynomials with integer coefficients: successive minima in $L_2(0,1)$","authors":"W. Banaszczyk","doi":"10.4064/ap190413-20-10","DOIUrl":"https://doi.org/10.4064/ap190413-20-10","url":null,"abstract":". Let P Z n be the additive subgroup of the real Hilbert space L 2 (0 , 1) consisting of polynomials of order ≤ n with integer coefficients. We may treat P Z n as a lattice in ( n + 1) -dimensional Euclidean space; let λ i ( P Z n ) ( 1 ≤ i ≤ n + 1 ) be the corresponding successive minima. We give rather precise estimates of λ i ( P Z n ) for i (cid:38) 23 n .","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70579269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We obtain some eigenvalue comparison theorems for Finsler manifolds with integral Ricci curvature bound.
． 得到了具有积分Ricci曲率界的Finsler流形的特征值比较定理。
{"title":"Eigenvalue comparison theorems for Finsler manifolds with integral Ricci curvature bound","authors":"B. Wu","doi":"10.4064/ap191208-16-5","DOIUrl":"https://doi.org/10.4064/ap191208-16-5","url":null,"abstract":". We obtain some eigenvalue comparison theorems for Finsler manifolds with integral Ricci curvature bound.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70580002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We present an algorithm for counting points on a double octic Calabi– Yau threefold associated to a configuration of eight planes over a finite field based on the existence of an elliptic curve fibration.
{"title":"Counting points on double octic Calabi–Yau threefolds over finite fields","authors":"Aleksander Czarnecki","doi":"10.4064/ap200210-30-8","DOIUrl":"https://doi.org/10.4064/ap200210-30-8","url":null,"abstract":". We present an algorithm for counting points on a double octic Calabi– Yau threefold associated to a configuration of eight planes over a finite field based on the existence of an elliptic curve fibration.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70581039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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