{"title":"Convergence of Fourier Integrals of Functions in L2\u0000α(Rn)","authors":"J. Twomey","doi":"10.1353/mpr.2022.0003","DOIUrl":"https://doi.org/10.1353/mpr.2022.0003","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121872959","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 : 1900-01-01DOI: 10.3318/PRIA.2005.105.1.49
J. Twomey
{"title":"STRONG APPROXIMATE CONTINUITY PROPERTIES OF CERTAIN CONJUGATE FUNCTIONS","authors":"J. Twomey","doi":"10.3318/PRIA.2005.105.1.49","DOIUrl":"https://doi.org/10.3318/PRIA.2005.105.1.49","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122051982","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}
{"title":"GROUPS WITH FINITELY MANY NORMALIZERS OF NON-NILPOTENT SUBGROUPS","authors":"F. De Mari, F. de Giovanni","doi":"10.1353/mpr.2007.0013","DOIUrl":"https://doi.org/10.1353/mpr.2007.0013","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117266947","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 : 1900-01-01DOI: 10.3318/PRIA.2010.110.1.83
M. Toumi
The only topology on vector lattices under consideration is the relatively uniform topology. Let A be vector lattice and let B be a topological space. A map P : A ?> B is called a homogeneous polynomial of degree n (or a n-homogeneous polynomial) if P (x) = $ (x,x), where ^ is a n-multilinear map from An = A x ... x A (n-times) into B. Throughout the paper, 'operator' (linear, multilinear or polynomial) will mean 'continuous operator'. A homogeneous polynomial (of degree n) P : A ?> B is said to be orthogonally additive if P(x + y) ? P(x) -f P(y) whenever x, y G A are orthogonally (i.e. x A y = 0). We denote by P0 (nA, B) the set of n-homogeneous orthogonally additive polynomials from A to B. Interest in orthogonally additive polynomials on Banach lattices originates in the work of K. Sundaresan [15], in which it has been characterised as the space of n-homogeneous orthogonally additive polynomials on Lp and ?p. More precisely, K. Sundaresan proved that every n-homogeneous orthogonally additive polynomial P : Lp -? R is determined by some g G L~ via the formula P (f) ? f fng d/i, for all / G Lp. Very recently, D. Perez-Garcia and I. Villanueva in [13], D. Carando, S. Lassalle and I. Zalduendo in [9] proved the following analogous result for C (X) spaces: Let Y be a Banach space, let P : C (X) ?> Y be an orthogonally additive
所考虑的向量格上的唯一拓扑是相对一致的拓扑。设A是向量晶格，设B是拓扑空间。如果P (x) = $ (x,x)，则映射P: A ?> B称为n次齐次多项式(或n次齐次多项式)，其中^是An = A x…在本文中，“算子”(线性的、多元线性的或多项式的)将意味着“连续算子”。(n次)齐次多项式P: A ?> B，如果P(x + y) ?P(x) -f P(y)，当x, y, G, A是正交的(即x A y = 0)。我们用P0 (nA, B)表示从A到B的n个齐次正交可加多项式的集合。对巴拿赫格上的正交可加多项式的兴趣起源于K. Sundaresan[15]的工作，其中它被表征为Lp和? P上n个齐次正交可加多项式的空间。更准确地说，K. Sundaresan证明了每一个n齐次正交可加多项式P: Lp -?R由某个g g L~通过公式P (f) ?f / d/i, for all / G Lp。最近，D. Perez-Garcia和I. Villanueva在[13]中，D. Carando, S. Lassalle和I. Zalduendo在[9]中证明了C (X)空间的如下类似结果:设Y是一个Banach空间，设P: C (X) ?> Y是一个正交加性
{"title":"ORTHOGONALLY ADDITIVE POLYNOMIALS ON DEDEKIND σ-COMPLETE VECTOR LATTICES","authors":"M. Toumi","doi":"10.3318/PRIA.2010.110.1.83","DOIUrl":"https://doi.org/10.3318/PRIA.2010.110.1.83","url":null,"abstract":"The only topology on vector lattices under consideration is the relatively uniform topology. Let A be vector lattice and let B be a topological space. A map P : A ?> B is called a homogeneous polynomial of degree n (or a n-homogeneous polynomial) if P (x) = $ (x,x), where ^ is a n-multilinear map from An = A x ... x A (n-times) into B. Throughout the paper, 'operator' (linear, multilinear or polynomial) will mean 'continuous operator'. A homogeneous polynomial (of degree n) P : A ?> B is said to be orthogonally additive if P(x + y) ? P(x) -f P(y) whenever x, y G A are orthogonally (i.e. x A y = 0). We denote by P0 (nA, B) the set of n-homogeneous orthogonally additive polynomials from A to B. Interest in orthogonally additive polynomials on Banach lattices originates in the work of K. Sundaresan [15], in which it has been characterised as the space of n-homogeneous orthogonally additive polynomials on Lp and ?p. More precisely, K. Sundaresan proved that every n-homogeneous orthogonally additive polynomial P : Lp -? R is determined by some g G L~ via the formula P (f) ? f fng d/i, for all / G Lp. Very recently, D. Perez-Garcia and I. Villanueva in [13], D. Carando, S. Lassalle and I. Zalduendo in [9] proved the following analogous result for C (X) spaces: Let Y be a Banach space, let P : C (X) ?> Y be an orthogonally additive","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"3 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128781675","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 : 1900-01-01DOI: 10.3318/pria.2019.119.11
Bunce, Timoney
{"title":"On decompositions of ternary rings of operators and their\u0000 morphisms","authors":"Bunce, Timoney","doi":"10.3318/pria.2019.119.11","DOIUrl":"https://doi.org/10.3318/pria.2019.119.11","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128996012","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 : 1900-01-01DOI: 10.3318/PRIA.2011.112.07
K. Izuchi, Y. Izuchi, S. Ohno
Let H2 be the Hardy space and H°° the Banach space of bounded analytic functions on the open unit disk ID with the supremum norm || • Hoc. For / £ H°°, we denote by /* the radial limit of / defined a.e. on the boundary 3D of P. We write {|/*| = 1} = {el° £ 3D : f*(ete) — 1}. Let m be the normalized Lebesgue measure on 3D. We denote by 5#* the set of analytic self-maps of D and Sh^.o — G Sh=c : Hvlloo = !}• For p £ Shthe composition operator C^ on H2 is defined by C^f = f o tp for / £ H2. Let C(H2) be the space of composition operators on H2 with the operator norm. The most interesting subject in the study of C(H2) is called the connected component problem, describing the connected component containing a given Cv. It was first studied by Berkson [2]. He showed that if p € 0, then is an isolated point in C(H2). Around 1990, MacCluer [13] and Shapiro and Sundberg [19] revisited the connected component problem on H2. Succeedingly, Bourdon [3], Gallardo-Gutierrez, Gonzalez, Nieminen and Saksman [6] and Moorhouse and Toews [16] followed. Still it remains unclear the connected component problem on H2 (see [4; 17; 18]). Similarly we have the space C(H°°) of composition operators on H°° with the
设H2为开放单元盘ID上具有上范数的有界解析函数的Hardy空间，H°°为Banach空间。对于/£H°°，我们用/*表示/定义的a.e.在p的边界3D上的径向极限。我们写{|/*| = 1}= {el°£3D: f*(ete) - 1}。设m为三维上的归一化勒贝格测度。我们用5#*表示D和Sh^的解析自映射集。o - G Sh=c: Hvlloo = !}•对于p£Sh，复合算子c ^ on H2定义为c ^f = fo tp For /£H2。设C(H2)是H2上具有算子范数的复合算子的空间。研究C(H2)中最有趣的问题是连通分量问题，它描述了含有给定Cv的连通分量。最早由Berkson研究[2]。他证明了如果p€0，那么是C(H2)中的一个孤立点。1990年前后，MacCluer[13]和Shapiro and Sundberg[19]重新研究了H2上的连通分量问题。随后，Bourdon[3]、Gallardo-Gutierrez、Gonzalez、Nieminen and Saksman[6]、Moorhouse and Toews[16]也相继提出了类似的观点。H2上的连通分量问题仍然不清楚(参见[4];17;18])。类似地，我们有复合算子的空间C(H°)在H°上
{"title":"PATH CONNECTED COMPONENTS IN THE SPACE OF WEIGHTED COMPOSITION OPERATORS ON THE DISK ALGEBRA","authors":"K. Izuchi, Y. Izuchi, S. Ohno","doi":"10.3318/PRIA.2011.112.07","DOIUrl":"https://doi.org/10.3318/PRIA.2011.112.07","url":null,"abstract":"Let H2 be the Hardy space and H°° the Banach space of bounded analytic functions on the open unit disk ID with the supremum norm || • Hoc. For / £ H°°, we denote by /* the radial limit of / defined a.e. on the boundary 3D of P. We write {|/*| = 1} = {el° £ 3D : f*(ete) — 1}. Let m be the normalized Lebesgue measure on 3D. We denote by 5#* the set of analytic self-maps of D and Sh^.o — G Sh=c : Hvlloo = !}• For p £ Shthe composition operator C^ on H2 is defined by C^f = f o tp for / £ H2. Let C(H2) be the space of composition operators on H2 with the operator norm. The most interesting subject in the study of C(H2) is called the connected component problem, describing the connected component containing a given Cv. It was first studied by Berkson [2]. He showed that if p € 0, then is an isolated point in C(H2). Around 1990, MacCluer [13] and Shapiro and Sundberg [19] revisited the connected component problem on H2. Succeedingly, Bourdon [3], Gallardo-Gutierrez, Gonzalez, Nieminen and Saksman [6] and Moorhouse and Toews [16] followed. Still it remains unclear the connected component problem on H2 (see [4; 17; 18]). Similarly we have the space C(H°°) of composition operators on H°° with the","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130511824","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 : 1900-01-01DOI: 10.3318/PRIA.2008.108.2.111
Emil Sköldberg
{"title":"A CONTRACTING HOMOTOPY FOR BARDZELL'S RESOLUTION","authors":"Emil Sköldberg","doi":"10.3318/PRIA.2008.108.2.111","DOIUrl":"https://doi.org/10.3318/PRIA.2008.108.2.111","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126958633","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 : 1900-01-01DOI: 10.3318/PRIA.2004.104.1.119
F. Barry
The commutator subgroup G' can indicate if a finite group G is a CLT (Converse Lagrange's Theorem) group or an NCLT (Non-Converse Lagrange's Theorem) group. We give general results and some examples of their application to groups of small order.
{"title":"THE COMMUTATOR SUBGROUP AND CLT(NCLT) GROUPS","authors":"F. Barry","doi":"10.3318/PRIA.2004.104.1.119","DOIUrl":"https://doi.org/10.3318/PRIA.2004.104.1.119","url":null,"abstract":"The commutator subgroup G' can indicate if a finite group G is a CLT (Converse Lagrange's Theorem) group or an NCLT (Non-Converse Lagrange's Theorem) group. We give general results and some examples of their application to groups of small order.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132230151","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 : 1900-01-01DOI: 10.3318/PRIA.2008.108.2.149
B. Duggal
A Banach space operator T ∈ B(X ) is polaroid (left polaroid) if isolated points of the spectrum (resp., isolated points λ of the approximate point spectrum) of T are poles of the resolvent of T (resp., are such that (T − λI) has finite ascent ≤ d and (T − λI)X is closed). Necessary and sufficient conditions for operators T ∈ B(X ) to satisfy generalized and a-generalized Browder and Weyl theorems are given. In the case of polaroid (resp., left polaroid) operators T , it is proved that T satisfies generalized Weyl’s theorem (resp., generalized a–Weyl’s theorem) if and only if T satisfies Weyl’s theorem (resp., a–Weyl’s theorem).
{"title":"POLAROID OPERATORS AND GENERALIZED BROWDER-WEYL THEOREMS","authors":"B. Duggal","doi":"10.3318/PRIA.2008.108.2.149","DOIUrl":"https://doi.org/10.3318/PRIA.2008.108.2.149","url":null,"abstract":"A Banach space operator T ∈ B(X ) is polaroid (left polaroid) if isolated points of the spectrum (resp., isolated points λ of the approximate point spectrum) of T are poles of the resolvent of T (resp., are such that (T − λI) has finite ascent ≤ d and (T − λI)X is closed). Necessary and sufficient conditions for operators T ∈ B(X ) to satisfy generalized and a-generalized Browder and Weyl theorems are given. In the case of polaroid (resp., left polaroid) operators T , it is proved that T satisfies generalized Weyl’s theorem (resp., generalized a–Weyl’s theorem) if and only if T satisfies Weyl’s theorem (resp., a–Weyl’s theorem).","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"4 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132417930","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 : 1900-01-01DOI: 10.3318/PRIA.2005.105.2.51
H. P. Singh, Rajesh Singh, M. R. Espejo, M. D. Pineda, S. Nadarajah
AbstractThis article suggests a dual to ratio-cum-product estimator for flnite populationmean that is complementary, in a certain sense, to the commonly used ratio-cum-product estimator reported by Singh [4]. The expressions for bias and meansquare error of the proposed estimator have been obtained to the flrst degree ofapproximation. This study also generalises the work of Srivenkataramana [5] andBandyopadhyay [1]. To illustrate the results an empirical study is carried out.1. IntroductionLet U be a flnite population consisting of N units u 1 ;u 2 ;:::;u N . The units of thisflnite population are identiflable in the sense that they are uniquely labelled from1 to N and the label of each unit is known. Let y and ( x;z ) denote the studyvariate and auxiliary variates taking the values y i and ( x i ;z i ), respectively, on theunit u i ( i = 1 ; 2 ;:::;N ), where x is positively correlated with y and z is negativelycorrelated with y . We wish to estimate the population mean Y„ = (1 =N )P Ni =1
摘要本文提出了一个有限种群均值的对偶比积估计量，它在一定意义上补充了Singh[4]报道的常用的比积估计量。得到了该估计器的偏置和均方误差的一级近似表达式。本研究也推广了Srivenkataramana[5]和bandyopadhyay[1]的工作。为了说明结果，进行了实证研究。设U为由N个单位组成的有限种群U 1; U 2;:::; U N。这个种群的单位是可识别的，因为它们被唯一地标记为从1到N，并且每个单位的标签是已知的。设y和(x;z)分别表示取y i和(xi;z i)值的研究变量和辅助变量，在单位u i (i = 1;2;:::;N)，其中x与y正相关，z与y负相关。我们希望估计总体均值Y " = (1 =N)P Ni =1
{"title":"ON THE EFFICIENCY OF A DUAL TO RATIO-CUM-PRODUCT ESTIMATOR IN SAMPLE SURVEYS","authors":"H. P. Singh, Rajesh Singh, M. R. Espejo, M. D. Pineda, S. Nadarajah","doi":"10.3318/PRIA.2005.105.2.51","DOIUrl":"https://doi.org/10.3318/PRIA.2005.105.2.51","url":null,"abstract":"AbstractThis article suggests a dual to ratio-cum-product estimator for flnite populationmean that is complementary, in a certain sense, to the commonly used ratio-cum-product estimator reported by Singh [4]. The expressions for bias and meansquare error of the proposed estimator have been obtained to the flrst degree ofapproximation. This study also generalises the work of Srivenkataramana [5] andBandyopadhyay [1]. To illustrate the results an empirical study is carried out.1. IntroductionLet U be a flnite population consisting of N units u 1 ;u 2 ;:::;u N . The units of thisflnite population are identiflable in the sense that they are uniquely labelled from1 to N and the label of each unit is known. Let y and ( x;z ) denote the studyvariate and auxiliary variates taking the values y i and ( x i ;z i ), respectively, on theunit u i ( i = 1 ; 2 ;:::;N ), where x is positively correlated with y and z is negativelycorrelated with y . We wish to estimate the population mean Y„ = (1 =N )P Ni =1","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130197306","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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