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Constructive Mathematical Analysis最新文献

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Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields 一类grushin型向量场的无穷拉普拉斯黏性解的存在唯一性
Constructive Mathematical Analysis Pub Date : 2023-06-15 DOI: 10.33205/cma.1245581
Thomas Bieske, Zachary Forrest
{"title":"Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields","authors":"Thomas Bieske, Zachary Forrest","doi":"10.33205/cma.1245581","DOIUrl":"https://doi.org/10.33205/cma.1245581","url":null,"abstract":"In this paper we pose the $infty$-Laplace Equation as a Dirichlet Problem in a class of Grushin-type spaces whose vector fields are of the form\u0000 begin{equation*}\u0000 X_k(p):=sigma_k(p)frac{partial}{partial x_k}\u0000 end{equation*}\u0000 and $sigma_k$ is not a polynomial for indices $m+1 leq k leq n$. Solutions to the $infty$-Laplacian in the viscosity sense have been shown to exist and be unique in [3], when $sigma_k$ is a polynomial; we extend these results by exploiting the relationship between Grushin-type and Euclidean second-order jets and utilizing estimates on the viscosity derivatives of sub- and supersolutions in order to produce a comparison principle for semicontinuous functions.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43740791","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
King operators which preserve $x^j$ 保留$x^j的King运算符$
Constructive Mathematical Analysis Pub Date : 2023-06-15 DOI: 10.33205/cma.1259505
Z. Finta
{"title":"King operators which preserve $x^j$","authors":"Z. Finta","doi":"10.33205/cma.1259505","DOIUrl":"https://doi.org/10.33205/cma.1259505","url":null,"abstract":"We prove the unique existence of the functions $r_n$ $(n=1,2,ldots )$ on $[0,1]$ such that the corresponding sequence of King operators approximates each continuous function on $[0,1]$ and preserves the functions $e_0(x)=1$ and $e_j(x)=x^j$, where $jin{ 2,3,ldots}$ is fixed. We establish the essential properties of $r_n$, and the rate of convergence of the new sequence of King operators will be estimated by the usual modulus of continuity. Finally, we show that the introduced operators are not polynomial and we obtain quantitative Voronovskaja type theorems for these operators.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47398396","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 an interpolation sequence for a weighted Bergman space on a Hilbert unit ball Hilbert单位球上加权Bergman空间的插值序列
Constructive Mathematical Analysis Pub Date : 2023-06-03 DOI: 10.33205/cma.1240126
Mohammed EL AIDI
{"title":"On an interpolation sequence for a weighted Bergman space on a Hilbert unit ball","authors":"Mohammed EL AIDI","doi":"10.33205/cma.1240126","DOIUrl":"https://doi.org/10.33205/cma.1240126","url":null,"abstract":"The purpose is to provide a generalization of Carleson's Theorem on interpolating sequences when dealing with a sequence in the open unit ball of a Hilbert space. Precisely, we interpolate a sequence by a function belonging to a weighted Bergman space of infinite order on a unit Hilbert ball and we furnish explicitly the upper bound corresponding to the interpolation constant.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46335279","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
Moving least squares approximation using variably scaled discontinuous weight function 使用可变缩放的不连续权函数的移动最小二乘逼近
Constructive Mathematical Analysis Pub Date : 2023-03-15 DOI: 10.33205/cma.1247239
Mohammad KARİMNEJAD ESFAHANİ, Stefano DE MARCHI, Francesco MARCHETTİ
{"title":"Moving least squares approximation using variably scaled discontinuous weight function","authors":"Mohammad KARİMNEJAD ESFAHANİ, Stefano DE MARCHI, Francesco MARCHETTİ","doi":"10.33205/cma.1247239","DOIUrl":"https://doi.org/10.33205/cma.1247239","url":null,"abstract":"Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable piecewise Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135598694","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
Construction of rational interpolations using Mamquist-Takenaka systems 利用Mamquist-Takenaka系统构造有理插值
Constructive Mathematical Analysis Pub Date : 2023-03-10 DOI: 10.33205/cma.1251068
F. Weisz
{"title":"Construction of rational interpolations using Mamquist-Takenaka systems","authors":"F. Weisz","doi":"10.33205/cma.1251068","DOIUrl":"https://doi.org/10.33205/cma.1251068","url":null,"abstract":"Rational functions have deep system-theoretic significance. They represent the natural way of modeling linear dynamical systems in the frequency (Laplace) domain. Using rational functions, the goal of this paper to compute models that match (interpolate) given data sets of measurements. In this paper, the authors show that using special rational orthonormal systems, the Malmquist-Takenaka systems, it is possible to write the rational interpolant $r_{(n, m)}$, for $n=N-1, m=N$ using only $N$ sampling nodes (instead of $2N$ nodes) if the interpolating nodes are in the complex unit circle or on the upper half-plane. Moreover, the authors prove convergence results related to the rational interpolant. They give an efficient algorithm for the determination of the rational interpolant.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48133956","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
Branched continued fraction representations of ratios of Horn's confluent function $mathrm{H}_6$ Horn的合流函数$ mathm {H}_6$比率的分支连分式表示
Constructive Mathematical Analysis Pub Date : 2023-03-06 DOI: 10.33205/cma.1243021
T. Antonova, R. Dmytryshyn, S. Sharyn
{"title":"Branched continued fraction representations of ratios of Horn's confluent function $mathrm{H}_6$","authors":"T. Antonova, R. Dmytryshyn, S. Sharyn","doi":"10.33205/cma.1243021","DOIUrl":"https://doi.org/10.33205/cma.1243021","url":null,"abstract":"In this paper, we derive some branched continued fraction representations for the ratios of the Horn's confluent function $mathrm{H}_6.$ The method employed is a two-dimensional generalization of the classical method of constructing of Gaussian continued fraction. We establish the estimates of the rate of convergence for the branched continued fraction expansions in some region $Omega$ (here, region is a domain (open connected set) together with all, part or none of its boundary). It is also proved that the corresponding branched continued fractions uniformly converge to holomorphic functions on every compact subset of some domain $Theta,$ and that these functions are analytic continuations of the ratios of double confluent hypergeometric series in $Theta.$ At the end, several numerical experiments are represented to indicate the power and efficiency of branched continued fractions as an approximation tool compared to double confluent hypergeometric series.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47890760","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
Banach-valued Bloch-type functions on the unit ball of a Hilbert space and weak spaces of Bloch-type Hilbert空间单位球上的Banach值Bloch型函数和Bloch型弱空间
Constructive Mathematical Analysis Pub Date : 2023-02-28 DOI: 10.33205/cma.1243686
T. Quang
{"title":"Banach-valued Bloch-type functions on the unit ball of a Hilbert space and weak spaces of Bloch-type","authors":"T. Quang","doi":"10.33205/cma.1243686","DOIUrl":"https://doi.org/10.33205/cma.1243686","url":null,"abstract":"In this article, we study the space $mathcal B_mu(B_X,Y)$ of $Y$-valued Bloch-type functions on the unit ball $B_X$ of an infinite dimensional Hilbert space $X$ with $mu$ is a normal weight on $B_X$ and $Y$ is a Banach space. We also investigate the characterizations of the space $mathcal{WB}_mu(B_X)$ of $Y$-valued, locally bounded, weakly holomorphic functions associated with the Bloch-type space $mathcal B_mu(B_X)$ of scalar-valued functions in the sense that $fin mathcal{WB}_mu(B_X)$ if $wcirc f in mathcal B_mu(B_X)$ for every $w in mathcal W,$ a separating subspace of the dual $Y'$ of $Y.$","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45854803","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
Beyond Descartes’ rule of signs 超越了笛卡儿的符号法则
Constructive Mathematical Analysis Pub Date : 2023-02-10 DOI: 10.33205/cma.1252639
V. Kostov
{"title":"Beyond Descartes’ rule of signs","authors":"V. Kostov","doi":"10.33205/cma.1252639","DOIUrl":"https://doi.org/10.33205/cma.1252639","url":null,"abstract":"We consider real univariate polynomials with all roots real. Such a polynomial with c sign changes and p sign preservations in the sequence of its coefficients has c positive and p negative roots counted with multiplicity. Suppose that all moduli of roots are distinct; we consider them as ordered on the positive half-axis. We ask the question: If the positions of the sign changes are known, what can the positions of the moduli of negative roots be? We prove several new results which show how far from trivial the answer to this question is.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42598288","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
Directs estimates and a Voronovskaja-type formula for Mihesan operators Mihesan算子的Directs估计和Voronovskaja型公式
Constructive Mathematical Analysis Pub Date : 2022-12-01 DOI: 10.33205/cma.1169884
J. Bustamante
{"title":"Directs estimates and a Voronovskaja-type formula for Mihesan operators","authors":"J. Bustamante","doi":"10.33205/cma.1169884","DOIUrl":"https://doi.org/10.33205/cma.1169884","url":null,"abstract":"We present an estimate for the rate of convergence of Mihesan operators in polynomial weighted spaces. A Voronovskaja-type theorem is included.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44082330","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
Exponential approximation in variable exponent Lebesgue spaces on the real line 实数上变指数Lebesgue空间的指数逼近
Constructive Mathematical Analysis Pub Date : 2022-12-01 DOI: 10.33205/cma.1167459
R. Akgün
{"title":"Exponential approximation in variable exponent Lebesgue spaces on the real line","authors":"R. Akgün","doi":"10.33205/cma.1167459","DOIUrl":"https://doi.org/10.33205/cma.1167459","url":null,"abstract":"Present work contains a method to obtain Jackson and Stechkin type inequalities of approximation by integral functions of finite degree (IFFD) in some variable exponent Lebesgue space of real functions defined on $boldsymbol{R}:=left( -infty ,+infty right) $. To do this, we employ a transference theorem which produce norm inequalities starting from norm inequalities in $mathcal{C}(boldsymbol{R})$, the class of bounded uniformly continuous functions defined on $boldsymbol{R}$. Let $Bsubseteq boldsymbol{R}$ be a measurable set, $pleft( xright) :Brightarrow lbrack 1,infty )$ be a measurable function. For the class of functions $f$ belonging to variable exponent Lebesgue spaces $L_{pleft( xright) }left( Bright) $, we consider difference operator $left( I-T_{delta }right)^{r}fleft( cdot right) $ under the condition that $p(x)$ satisfies the log-Hölder continuity condition and $1leq mathop{rm ess ; inf} limitsnolimits_{xin B}p(x)$, $mathop{rm ess ; sup}limitsnolimits_{xin B}p(x)<infty $, where $I$ is the identity operator, $rin mathrm{N}:=left{ 1,2,3,cdots right} $, $delta geq 0$ and\u0000 $$\u0000 T_{delta }fleft( xright) =frac{1}{delta }intnolimits_{0}^{delta\u0000 }fleft( x+tright) dt, xin boldsymbol{R},\u0000 T_{0}equiv I,\u0000 $$\u0000 is the forward Steklov operator. It is proved that\u0000 $$\u0000 leftVert left( I-T_{delta }right) ^{r}frightVert _{pleft( cdot\u0000 right) }\u0000 $$\u0000 is a suitable measure of smoothness for functions in $L_{pleft( xright)\u0000 }left( Bright) $, where $leftVert cdot rightVert _{pleft( cdot\u0000 right) }$ is Luxemburg norm in $L_{pleft( xright) }left( Bright) .$ We\u0000 obtain main properties of difference operator $leftVert left( I-T_{delta\u0000 }right) ^{r}frightVert _{pleft( cdot right) }$ in $L_{pleft( xright)\u0000 }left( Bright) .$ We give proof of direct and inverse theorems of\u0000 approximation by IFFD in $L_{pleft( xright) }left( boldsymbol{R}right)\u0000 . $","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45265452","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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