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Moroccan Journal of Pure and Applied Analysis最新文献

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Volterra operator norms : a brief survey 沃尔泰拉运营商规范:简要调查
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0018
T. Ransford
{"title":"Volterra operator norms : a brief survey","authors":"T. Ransford","doi":"10.2478/mjpaa-2023-0018","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0018","url":null,"abstract":"Abstract In this expository article, we discuss the evaluation and estimation of the operator norms of various functions of the Volterra operator.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"276 - 290"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42142474","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
Mohamed Zarrabi 1964-2021 穆罕默德·扎拉比1964-2021
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0011
Omar El Fallah, K. Kellay, Ouhabaz El Maati
{"title":"Mohamed Zarrabi 1964-2021","authors":"Omar El Fallah, K. Kellay, Ouhabaz El Maati","doi":"10.2478/mjpaa-2023-0011","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0011","url":null,"abstract":"Abstract This note is dedicated to recalling the virtues and the important contributions in mathematics of mohamed zarabi who passed a way on mid december 2021.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"154 - 156"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47843094","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
Negative Powers of Contractions Having a Strong AA+ Spectrum 具有强AA+谱的负收缩力
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0015
J. Esterle
{"title":"Negative Powers of Contractions Having a Strong AA+ Spectrum","authors":"J. Esterle","doi":"10.2478/mjpaa-2023-0015","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0015","url":null,"abstract":"Abstract Zarrabi proved in 1993 that if the spectrum of a contraction T on a Banach space is a countable subset of the unit circle 𝕋, and if limn→+∞log(‖ T−n ‖)n=0 {lim _{n to + infty }}{{log left( {left| {{T^{ - n}}} right|} right)} over {sqrt n }} = 0 , then T is an isometry, so that ‖Tn‖ = 1 for every n ∈ ℤ. It is also known that if C is the usual triadic Cantor set then every contraction T on a Banach space such that Spec(T ) ⊂ 𝒞 satisfying lim supn→+∞log(‖ T−n ‖)nα<+∞ lim ,su{p_{n to + infty }}{{log left( {left| {{T^{ - n}}} right|} right)} over {{n^alpha }}} < + infty for some α<log(3)−log(2)2 log(3)−log(2) alpha < {{log left( 3 right) - log left( 2 right)} over {2,log left( 3 right) - log left( 2 right)}} is an isometry. In the other direction an easy refinement of known results shows that if a closed E ⊂ 𝕋 is not a “strong AA+-set” then for every sequence (un)n≥1 of positive real numbers such that lim infn→+∞un = + ∞ there exists a contraction T on some Banach space such that Spec(T )⊂ E, ‖T−n‖ = O(un) as n → + ∞ and supn≥1 ‖T−n‖ = + ∞. We show conversely that if E ⊂ 𝕋 is a strong AA+-set then there exists a nondecreasing unbounded sequence (un)n≥1 such that for every contraction T on a Banach space satsfying Spec(T) ⊂ E and ‖T−n ‖ = O(un) as n → + ∞ we have supn>0 ‖T−n ‖ ≤ K, where K < + ∞ denotes the “AA+-constant” of E (closed countanble subsets of 𝕋 and the triadic Cantor set are strong AA+-sets of constant 1).","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"209 - 215"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42518556","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
On the Cyclicity of Dilated Systems in Lattices: Multiplicative Sequences, Polynomials, Dirichlet-type Spaces and Algebras 格中扩张系统的循环性:乘法序列、多项式、狄利克雷型空间和代数
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0017
N. Nikolski
{"title":"On the Cyclicity of Dilated Systems in Lattices: Multiplicative Sequences, Polynomials, Dirichlet-type Spaces and Algebras","authors":"N. Nikolski","doi":"10.2478/mjpaa-2023-0017","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0017","url":null,"abstract":"Abstract The aim of these notes is to discuss the completeness of the dilated systems in a most general framework of an arbitrary sequence lattice X, including weighted ℓp spaces. In particular, general multiplicative and completely multiplicative sequences are treated. After the Fourier–Bohr transformation, we deal with the cyclicity property in function spaces on the corresponding infinite dimensional Reinhardt domain 𝔻X∞ mathbb{D}_X^infty . Functions with (weakly) dominating free term and (in particular) linearly factorable functions are considered. The most attention is paid to the cases of the polydiscs 𝔻X∞,|ℂN=𝔻N mathbb{D}_X^infty ,|{mathbb{C}^N} = {mathbb{D}^N} and the ℓp-unit balls 𝔻X∞,|ℂN=𝔹pN mathbb{D}_X^infty ,|{mathbb{C}^N} = mathbb{B}_p^N , in particular to Dirichlet-type and Dirichlet–Drury–Arveson-type spaces and algebras, as X=ℓp(ℤ+N,(1+α)s) X = {ell ^p}left( {_ + ^N,{{left( {1 + alpha } right)}^s}} right)) , s = (s1, s2, … ) and X=ℓp(ℤ+N,  (α!| α |!)t(1+| α |)s) X = {ell ^p}left( {mathbb{Z}_ + ^N,,,{{left( {{{alpha !} over {left| alpha right|!}}} right)}^t}{{left( {1 + left| alpha right|} right)}^s}} right) , s,t ≥ 0, as well as to their infinite variables analogues. We priviledged the largest possible scale of spaces and the most elementary instruments used.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"238 - 275"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48971112","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
H∞ interpolation constrained by Beurling–Sobolev norms Beurling–Sobolev范数约束的H∞插值
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0012
A. Baranov, R. Zarouf
{"title":"H∞ interpolation constrained by Beurling–Sobolev norms","authors":"A. Baranov, R. Zarouf","doi":"10.2478/mjpaa-2023-0012","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0012","url":null,"abstract":"Abstract We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc, constrained by Beurling–Sobolev norms. We find sharp asymptotics of the corresponding interpolation quantities, thereby improving the known estimates. On our way we obtain a S. M. Nikolskii type inequality for rational functions whose poles lie outside of the unit disc. It shows that the embedding of the Hardy space H2 into the Wiener algebra of absolutely convergent Fourier/Taylor series is invertible on the subset of rational functions of a given degree, whose poles remain at a given distance from the unit circle.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"157 - 167"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49548913","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
Sums and products of periodic functions 周期函数的和与积
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0014
R. Deville
{"title":"Sums and products of periodic functions","authors":"R. Deville","doi":"10.2478/mjpaa-2023-0014","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0014","url":null,"abstract":"Abstract There exist two real valued periodic functions on the real line such that, for every x ∈ ℝ, f1(x) + f2(x) = x, but it is impossible to find two real valued periodic functions on the real line such that, for every x ∈ ℝ, f1(x) + f2(x) = x2. The purpose of this note is to prove this result and also to study the possibility of decomposing more general polynomials into sum of periodic functions.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"204 - 208"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43906572","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 Maximum Locus of the Bloch Norm Bloch范数的最大轨迹
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI: 10.2478/mjpaa-2023-0019
Youssfi El Hassan
{"title":"The Maximum Locus of the Bloch Norm","authors":"Youssfi El Hassan","doi":"10.2478/mjpaa-2023-0019","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0019","url":null,"abstract":"Abstract For a Bloch function f in the unit ball in ℂn, we study the maximal locus of the Bloch norm of f; namely, the set Lf where the Bergman length of the gradient vector field of f attains its maximum. We prove that for n ≥, the set Lf consists of a finite union of real analytic sets with dimensions at most 2n − 2. This is not the case for n = 1 as was proved earlier by Cima and Wogen. We also give some rigidity properties of the set Lf. In particular, we give some sufficient criteria for constructing extreme functions in the Little Bloch ball.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"291 - 303"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46562742","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
Carleson’s formula for some weighted Dirichlet spaces 一些加权Dirichlet空间的Carleson公式
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-01-24 DOI: 10.2478/mjpaa-2023-0013
B. Bouya, A. Hartmann
{"title":"Carleson’s formula for some weighted Dirichlet spaces","authors":"B. Bouya, A. Hartmann","doi":"10.2478/mjpaa-2023-0013","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0013","url":null,"abstract":"Abstract We extend Carleson’s formula to radially polynomially weighted Dirichlet spaces.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"168 - 203"},"PeriodicalIF":0.0,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48058388","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
New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems FGM二元copuln的新非对称扰动及一致性保持问题
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.2478/mjpaa-2023-0008
Mohamed El maazouz, A. Sani
{"title":"New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems","authors":"Mohamed El maazouz, A. Sani","doi":"10.2478/mjpaa-2023-0008","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0008","url":null,"abstract":"Abstract New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"111 - 126"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48830060","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
Parameters identification for a nonlinear partial differential equation in image denoising 图像去噪中非线性偏微分方程的参数辨识
Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.2478/mjpaa-2023-0010
A. E. Mourabit
{"title":"Parameters identification for a nonlinear partial differential equation in image denoising","authors":"A. E. Mourabit","doi":"10.2478/mjpaa-2023-0010","DOIUrl":"https://doi.org/10.2478/mjpaa-2023-0010","url":null,"abstract":"Abstract In this work and in the context of PDE constrained optimization problems, we are interested in identification of a parameter in the diffusion equation proposed in [1]. We propose to identify this parameter automatically by a gradient descent algorithm to improve the restoration of a noisy image. Finally, we give numerical results to illustrate the performance of the automatic selection of this parameter and compare our numerical results with other image denoising approaches or algorithms.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"9 1","pages":"141 - 153"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47007283","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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