Extreme symmetric norms on $R^2$

Ryszard Grząślewicz

Displaying similar documents to “Extreme symmetric norms on $R^{2}$ ”

Scalar differential concomitants of first order of a symmetric connexion $Γ_{j k}^{i}$ in the two-dimensional space and their applications

Michał Lorens (1980)

Annales Polonici Mathematici

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Extreme operators on 2-dimensional $l_{p}$ -spaces

Ryszard Grząślewicz (1981)

Colloquium Mathematicae

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$H^{p}$ spaces on bounded symmetric domains

Kyong T. Hahn, Josephine Mitchell (1973)

Annales Polonici Mathematici

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Symmetric products of the Euclidean spaces and the spheres

Naotsugu Chinen (2015)

Commentationes Mathematicae Universitatis Carolinae

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By $F_{n} (X)$ , $n \geq 1$ , we denote the $n$ -th symmetric product of a metric space $(X, d)$ as the space of the non-empty finite subsets of $X$ with at most $n$ elements endowed with the Hausdorff metric $d_{H}$ . In this paper we shall describe that every isometry from the $n$ -th symmetric product $F_{n} (X)$ into itself is induced by some isometry from $X$ into itself, where $X$ is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the $n$ -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence...

Some properties of certain subclasses of bounded Mocanu variation with respect to $2 k$ -symmetric conjugate points

Rasoul Aghalary, Jafar Kazemzadeh (2019)

Mathematica Bohemica

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We introduce subclasses of analytic functions of bounded radius rotation, bounded boundary rotation and bounded Mocanu variation with respect to $2 k$ -symmetric conjugate points and study some of its basic properties.

On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag (2010)

Journal of the European Mathematical Society

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Suppose that $μ$ is an absolutely continuous probability measure on $^{R}$ n, for large $n$ . Then $μ$ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if $n \geq {(C / ε)}^{C d}$ , then there exist $d$ -dimensional marginals of $μ$ that are $ε$ -far from being sphericallysymmetric, in an appropriate sense. Here $C > 0$ is a universal constant.

Complex symmetry of Toeplitz operators on the weighted Bergman spaces

Xiao-He Hu (2022)

Czechoslovak Mathematical Journal

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We give a concrete description of complex symmetric monomial Toeplitz operators $T_{z^{p} {\bar{z}}^{q}}$ on the weighted Bergman space $A^{2} (Ω)$ , where $Ω$ denotes the unit ball or the unit polydisk. We provide a necessary condition for $T_{z^{p} {\bar{z}}^{q}}$ to be complex symmetric. When $p, q \in ℕ^{2}$ , we prove that $T_{z^{p} {\bar{z}}^{q}}$ is complex symmetric on $A^{2} (Ω)$ if and only if $p_{1} = q_{2}$ and $p_{2} = q_{1}$ . Moreover, we completely characterize when monomial Toeplitz operators $T_{z^{p} {\bar{z}}^{q}}$ on $A^{2} (𝔻_{n})$ are $J_{U}$ -symmetric with the $n \times n$ symmetric unitary matrix $U$ .

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II

Matthew Randall (2025)

Archivum Mathematicum

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We show the change of coordinates that maps the maximally symmetric $(2, 3, 5)$ -distribution given by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation and the corresponding Ricci-flat conformal scale...

Taylor towers of symmetric and exterior powers

Brenda Johnson, Randy McCarthy (2008)

Fundamenta Mathematicae

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We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, $D_{k} S p ⁿ$ and $D_{k} Λ ⁿ$ , in terms of the first terms in the Taylor towers of $S p^{t}$ and $Λ^{t}$ for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of $S p^{t}$ and $Λ^{t}$ . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for $D_{k} S p ⁿ$ and $D_{k} Λ ⁿ$ .

A note on average behaviour of the Fourier coefficients of $j$ th symmetric power $L$ -function over certain sparse sequence of positive integers

Youjun Wang (2024)

Czechoslovak Mathematical Journal

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Let $j \geq 2$ be a given integer. Let $H_{k}^{*}$ be the set of all normalized primitive holomorphic cusp forms of even integral weight $k \geq 2$ for the full modulo group $SL (2, ℤ)$ . For $f \in H_{k}^{*}$ , denote by $λ_{{sym}^{j} f} (n)$ the $n$ th normalized Fourier coefficient of $j$ th symmetric power $L$ -function ( $L (s, {sym}^{j} f)$ ) attached to $f$ . We are interested in the average behaviour of the sum $\sum_{\binom{n = a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} + a_{5}^{2} + a_{6}^{2} \leq x}{(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}) \in ℤ^{6}}} λ_{{sym}^{j} f}^{2} (n),$ where $x$ is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023).

Sharp Ratio Inequalities for a Conditionally Symmetric Martingale

Adam Osękowski (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let f be a conditionally symmetric martingale and let S(f) denote its square function. (i) For p,q > 0, we determine the best constants $C_{p, q}$ such that $s u p_{n} {(| f ₙ |}^{p} {) / (1 + S ₙ ² (f))}^{q} \leq C_{p, q}$ . Furthermore, the inequality extends to the case of Hilbert space valued f. (ii) For N = 1,2,... and q > 0, we determine the best constants $C_{N, q}^{'}$ such that $s u p_{n} (f ₙ^{2 N - 1}) {(1 + S ₙ ² (f))}^{q} \leq C_{N, q}^{'}$ . These bounds are extended to sums of conditionally symmetric variables which are not necessarily integrable. In addition, we show that neither of the inequalities above holds if...

Some properties for $α$ -starlike functions with respect to $k$ -symmetric points of complex order

H. E. Darwish, A. Y. Lashin, S. M. Sowileh (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In the present work, we introduce the subclass $𝒯_{γ, α}^{k} (ϕ)$ , of starlike functions with respect to $k$ -symmetric points of complex order $γ$ ( $γ \neq 0$ ) in the open unit disc . Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.

Product property for capacities in $ℂ^{N}$

Mirosław Baran, Leokadia Bialas-Ciez (2012)

Annales Polonici Mathematici

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The paper deals with logarithmic capacities, an important tool in pluripotential theory. We show that a class of capacities, which contains the L-capacity, has the following product property: $C_{ν} (E ₁ \times E ₂) = m i n (C_{ν ₁} (E ₁), C_{ν ₂} (E ₂))$ , where $E_{j}$ and $ν_{j}$ are respectively a compact set and a norm in $ℂ^{N_{j}}$ (j = 1,2), and ν is a norm in $ℂ^{N ₁ + N ₂}$ , ν = ν₁⊕ₚ ν₂ with some 1 ≤ p ≤ ∞. For a convex subset E of $ℂ^{N}$ , denote by C(E) the standard L-capacity and by $ω_{E}$ the minimal width of E, that is, the minimal Euclidean distance between two supporting hyperplanes...

The real symmetric matrices of odd order with a P-set of maximum size

Zhibin Du, Carlos Martins da Fonseca (2016)

Czechoslovak Mathematical Journal

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Suppose that $A$ is a real symmetric matrix of order $n$ . Denote by $m_{A} (0)$ the nullity of $A$ . For a nonempty subset $α$ of ${1, 2, ..., n}$ , let $A (α)$ be the principal submatrix of $A$ obtained from $A$ by deleting the rows and columns indexed by $α$ . When $m_{A (α)} (0) = m_{A} (0) + | α |$ , we call $α$ a P-set of $A$ . It is known that every P-set of $A$ contains at most $⌊ n / 2 ⌋$ elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As...

On the symmetric algebra of certain first syzygy modules

Gaetana Restuccia, Zhongming Tang, Rosanna Utano (2022)

Czechoslovak Mathematical Journal

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Let $(R, 𝔪)$ be a standard graded $K$ -algebra over a field $K$ . Then $R$ can be written as $S / I$ , where $I \subseteq {(x_{1}, ..., x_{n})}^{2}$ is a graded ideal of a polynomial ring $S = K [x_{1}, ..., x_{n}]$ . Assume that $n \geq 3$ and $I$ is a strongly stable monomial ideal. We study the symmetric algebra ${Sym}_{R} ({Syz}_{1} (𝔪))$ of the first syzygy module ${Syz}_{1} (𝔪)$ of $𝔪$ . When the minimal generators of $I$ are all of degree 2, the dimension of ${Sym}_{R} ({Syz}_{1} (𝔪))$ is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.

A characterization of the disc $D^{n}$

Th. Friedrich (1974)

Colloquium Mathematicae

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Displaying similar documents to “Extreme symmetric norms on R 2 ”

Displaying similar documents to “Extreme symmetric norms on $R^{2}$ ”