{"title":"Norm attaining multilinear forms on the spaces $c_0$ or $l_1$","authors":"Sung Guen Kim","doi":"10.33205/cma.981877","DOIUrl":"https://doi.org/10.33205/cma.981877","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48012114","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":"Oscillation of noncanonical second-order advanced differential equations via canonical transform","authors":"M. Bohner, K. Vidhyaa, E. Thandapani","doi":"10.33205/cma.1055356","DOIUrl":"https://doi.org/10.33205/cma.1055356","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45317439","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}
Abstract. Hilberdink showed that there exists a constant c0 > 2, such that there exists a continuous prim system satisfying N(x) = c(x − 1) + 1 if and only if c ≤ c0. Here we determine c0 numerically to be 1.25479 ·10 ±2 ·10 . To do so we compute a representation for a twisted exponential function as a sum over the roots of the Riemann zeta function. We then give explicit bounds for the error obtained when restricting the occurring sum to a finite number of zeros.
{"title":"Continuous prime systems satisfying N(x)=c(x-1)+1","authors":"J. Schlage-Puchta","doi":"10.33205/cma.817761","DOIUrl":"https://doi.org/10.33205/cma.817761","url":null,"abstract":"Abstract. Hilberdink showed that there exists a constant c0 > 2, such that there exists a continuous prim system satisfying N(x) = c(x − 1) + 1 if and only if c ≤ c0. Here we determine c0 numerically to be 1.25479 ·10 ±2 ·10 . To do so we compute a representation for a twisted exponential function as a sum over the roots of the Riemann zeta function. We then give explicit bounds for the error obtained when restricting the occurring sum to a finite number of zeros.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43259612","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}
We consider the set of monic real uni-variate polynomials of a given degree $d$ with non-vanishing coefficients, with given signs of the coefficients and with given quantities $pos$ of their positive and $neg$ of their negative roots (all roots are distinct). For $dgeq 6$ and for signs of the coefficients $(+,-,+,+,ldots ,+,+,-,+)$, we prove that the set of such polynomials having two positive, $d-4$ negative and two complex conjugate roots, is not connected. For $pos+negleq 3$ and for any $d$, we give the exhaustive answer to the question for which signs of the coefficients there exist polynomials with such values of $pos$ and $neg$.
{"title":"The disconnectedness of certain sets defined after uni-variate polynomials","authors":"V. Kostov","doi":"10.33205/cma.1111247","DOIUrl":"https://doi.org/10.33205/cma.1111247","url":null,"abstract":"We consider the set of monic real uni-variate polynomials of a given degree $d$ with non-vanishing coefficients, with given signs of the coefficients and with given quantities $pos$ of their positive and $neg$ of their negative roots (all roots are distinct). For $dgeq 6$ and for signs of the coefficients $(+,-,+,+,ldots ,+,+,-,+)$, we prove that the set of such polynomials having two positive, $d-4$ negative and two complex conjugate roots, is not connected. For $pos+negleq 3$ and for any $d$, we give the exhaustive answer to the question for which signs of the coefficients there exist polynomials with such values of $pos$ and $neg$.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45784855","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":"Differential1 ${e}$-structures for equivalences of $2$-nondegenerate Levi rank $1$ hypersurfaces $M_5 ⊂ C$","authors":"W. Foo, J. Merker","doi":"10.33205/cma.943426","DOIUrl":"https://doi.org/10.33205/cma.943426","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49295584","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":"Isomorphism problem in a special class of Banach function algebras and its application","authors":"Kiyoshi Shirayanagi","doi":"10.33205/cma.952056","DOIUrl":"https://doi.org/10.33205/cma.952056","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41678321","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}
We extend the classical van der Corput inequality to the real line. As a consequence, we obtain a simple proof of the Wiener-Wintner theorem for the $mathbb{R}$-action which assert that for any family of maps $(T_t)_{t in mathbb{R}}$ acting on the Lebesgue measure space $(Omega,{cal {A}},mu)$ where $mu$ is a probability measure and for any $tin mathbb{R}$, $T_t$ is measure-preserving transformation on measure space $(Omega,{cal {A}},mu)$ with $T_t circ T_s =T_{t+s}$, for any $t,sin mathbb{R}$. Then, for any $f in L^1(mu)$, there is a a single null set off which $displaystyle lim_{T rightarrow +infty} frac1{T}int_{0}^{T} f(T_tomega) e^{2 i pi theta t} dt$ exists for all $theta in mathbb{R}$. We further present the joining proof of the amenable group version of Wiener-Wintner theorem due to Weiss and Ornstein.
{"title":"van der Corput inequality for real line and Wiener-Wintner theorem for amenable groups","authors":"E. Abdalaoui","doi":"10.33205/cma.1029202","DOIUrl":"https://doi.org/10.33205/cma.1029202","url":null,"abstract":"We extend the classical van der Corput inequality to the real line. As a consequence, we obtain a simple proof of the Wiener-Wintner theorem for the $mathbb{R}$-action which assert that for any family of maps $(T_t)_{t in mathbb{R}}$ acting on the Lebesgue measure space $(Omega,{cal {A}},mu)$ where $mu$ is a probability measure and for any $tin mathbb{R}$, $T_t$ is measure-preserving transformation on measure space $(Omega,{cal {A}},mu)$ with $T_t circ T_s =T_{t+s}$, for any $t,sin mathbb{R}$. Then, for any $f in L^1(mu)$, there is a a single null set off which $displaystyle lim_{T rightarrow +infty} frac1{T}int_{0}^{T} f(T_tomega) e^{2 i pi theta t} dt$ exists for all $theta in mathbb{R}$. We further present the joining proof of the amenable group version of Wiener-Wintner theorem due to Weiss and Ornstein.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48384265","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}
We introduce a method to construct general multivariate positive definite kernels on a nonempty set X that employs a prescribed bounded completely monotone function and special multivariate functions on X. The method is consistent with a generalized version of Aitken’s integral formula for Gaussians. In the case where X is a cartesian product, the method produces nonseparable positive definite kernels that may be useful in multivariate interpolation. In addition, it can be interpreted as an abstract multivariate generalization of the well-established Gneiting’s model for constructing space-time covariances commonly cited in the literature. Many parametric models discussed in statistics can be interpreted as particular cases of the method.
{"title":"Matrix valued positive definite kernels related to the generalized Aitken's integral for Gaussians","authors":"V. Menegatto, C. P. Oliveira","doi":"10.33205/cma.964096","DOIUrl":"https://doi.org/10.33205/cma.964096","url":null,"abstract":"We introduce a method to construct general multivariate positive definite kernels on a nonempty set X that employs a prescribed bounded completely monotone function and special multivariate functions on X. The method is consistent with a generalized version of Aitken’s integral formula for Gaussians. In the case where X is a cartesian product, the method produces nonseparable positive definite kernels that may be useful in multivariate interpolation. In addition, it can be interpreted as an abstract multivariate generalization of the well-established Gneiting’s model for constructing space-time covariances commonly cited in the literature. Many parametric models discussed in statistics can be interpreted as particular cases of the method.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41673806","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}
In this paper, we present the duality theory for general weighted space of vector functions. We mention that a characterization of the dual of a weighted space of vector functions in the particular case $V subset C^{+} (X)$ is mentioned by J. B. Prolla in [6]. Also, we extend de Branges lemma in this new setting for convex cones of a weighted spaces of vector functions (Theorem 4.2). Using this theorem, we find various approximations results for weighted spaces of vector functions: Theorems 4.2-4.6 as well as Corollary 4.3. We mention also that a brief version of this paper, in the particular case $V subset C^{+} (X)$, is presented in [3], Chapter 2, subparagraph 2.5.
本文给出了广义向量函数加权空间的对偶理论。我们提到了J. B. Prolla在[6]中提到的在特殊情况下向量函数加权空间的对偶的一个表征$V 子集C^{+} (X)$。同时，我们在向量函数加权空间的凸锥的这种新设置中推广了de Branges引理(定理4.2)。利用这个定理，我们得到了向量函数加权空间的各种近似结果:定理4.2-4.6和推论4.3。我们还提到，本文的一个简短版本，在特殊情况下$V 子集C^{+} (X)$，在[3]，第2章，分段2.5中给出。
{"title":"APROXIMATION IN WEIGHTED SPACES OF VECTOR FUNCTIONS","authors":"G. Păltineanu, I. Bucur","doi":"10.33205/CMA.825986","DOIUrl":"https://doi.org/10.33205/CMA.825986","url":null,"abstract":"In this paper, we present the duality theory for general weighted space of vector functions. We mention that a characterization of the dual of a weighted space of vector functions in the particular case $V subset C^{+} (X)$ is mentioned by J. B. Prolla in [6]. Also, we extend de Branges lemma in this new setting for convex cones of a weighted spaces of vector functions (Theorem 4.2). Using this theorem, we find various approximations results for weighted spaces of vector functions: Theorems 4.2-4.6 as well as Corollary 4.3. We mention also that a brief version of this paper, in the particular case $V subset C^{+} (X)$, is presented in [3], Chapter 2, subparagraph 2.5.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69532123","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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