Properties on subclass of Sakaguchi type functions using a Mittag-Leffler type Poisson distribution series

Elumalai Krishnan Nithiyanandham; Bhaskara Srutha Keerthi

Displaying similar documents to “Properties on subclass of Sakaguchi type functions using a Mittag-Leffler type Poisson distribution series”

Mean field limit for the one dimensional Vlasov-Poisson equation

Maxime Hauray (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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We consider systems of $N$ particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the Vlasov-Poisson equation. Actually a rigorous proof of that convergence was given by Trocheris in [Tro86]. Here we shall give a simpler proof of this result, and explain why it implies the so-called “Propagation of molecular chaos”. More precisely, both...

S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case

Josefina Alvarez, Martha Guzmán-Partida, Urszula Skórnik (2003)

Studia Mathematica

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We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S’-convolutions. We characterize those tempered distribution that are S’-convolvable with the Poisson kernel in the Euclidean case and the product domain case....

On the global regularity of subcritical Euler–Poisson equations with pressure

Eitan Tadmor, Dongming Wei (2008)

Journal of the European Mathematical Society

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We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual $γ$ -law pressure, $γ \geq 1$ , admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the $2 \times 2$ $p$ -system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann invariants and density crosses an intrinsic critical threshold.

The Dixmier-Moeglin equivalence and a Gel’fand-Kirillov problem for Poisson polynomial algebras

K. R. Goodearl, S. Launois (2011)

Bulletin de la Société Mathématique de France

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The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only finitely many Poisson prime ideals invariant are obtained. Combined with previous work of the first-named author, this establishes the Poisson Dixmier-Moeglin equivalence for large classes of Poisson polynomial rings, including semiclassical limits of quantum...

Kontsevich Deformation Quantization on Lie Algebras

Nabiha Ben Amar, Mouna Chaabouni, Mabrouka Hfaiedh (2007)

Bollettino dell'Unione Matematica Italiana

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We consider Kontsevich star product on the dual $\mathfrak{g}^{*}$ of a general Lie algebra g equipped with the linear Poisson bracket. We show that this star product provides a deformation quantization by partial embeddings in the direction of the Poisson bracket.

A note on discriminating Poisson processes from other point processes with stationary inter arrival times

Gusztáv Morvai, Benjamin Weiss (2019)

Kybernetika

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We give a universal discrimination procedure for determining if a sample point drawn from an ergodic and stationary simple point process on the line with finite intensity comes from a homogeneous Poisson process with an unknown parameter. Presented with the sample on the interval $[0, t]$ the discrimination procedure $g_{t}$ , which is a function of the finite subsets of $[0, t]$ , will almost surely eventually stabilize on either POISSON or NOTPOISSON with the first alternative occurring if and only if the...

Cauchy-Poisson transform and polynomial inequalities

Mirosław Baran (2009)

Annales Polonici Mathematici

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We apply the Cauchy-Poisson transform to prove some multivariate polynomial inequalities. In particular, we show that if the pluricomplex Green function of a fat compact set E in $ℝ^{N}$ is Hölder continuous then E admits a Szegö type inequality with weight function $d i s t {(x, \partial E)}^{- (1 - κ)}$ with a positive κ. This can be viewed as a (nontrivial) generalization of the classical result for the interval E = [-1,1] ⊂ ℝ.

A note on n-ary Poisson brackets

Michor, Peter W., Vaisman, Izu

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An $n$ -ary Poisson bracket (or generalized Poisson bracket) on the manifold $M$ is a skew-symmetric $n$ -linear bracket ${, \dots,}$ of functions which is a derivation in each argument and satisfies the generalized Jacobi identity of order $n$ , i.e., $\sum_{σ \in S_{2 n - 1}} (sign σ) {{f_{σ_{1}}, \dots, f_{σ_{n}}}, f_{σ_{n + 1}}, \dots, f_{σ_{2 n - 1}}} = 0,$ $S_{2 n - 1}$ being the symmetric group. The notion of generalized Poisson bracket was introduced by et al. in [J. Phys. A, Math. Gen. 29, No. 7, L151–L157 (1996; Zbl 0912.53019) and J. Phys. A, Math. Gen. 30, No. 18, L607–L616 (1997; Zbl 0932.37056)]....

The structure of split regular Hom-Poisson algebras

María J. Aragón Periñán, Antonio J. Calderón Martín (2016)

Colloquium Mathematicae

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We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form...

Poisson's equation and characterizations of reflexivity of Banach spaces

Vladimir P. Fonf, Michael Lin, Przemysław Wojtaszczyk (2011)

Colloquium Mathematicae

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Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder’s equality $x \in X : s u p_{n} | | \sum_{k = 1}^{n} T^{k} x | | < \infty$ = (I-T)X $.$ We then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup $T_{t} : t \geq 0$ with generator A satisfies $A X = x \in X : s u p_{s > 0} | | \int_{0}^{s} T_{t} x d t | | < \infty$ . The range (I-T)X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson’s equation (I-T)y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities...

Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series

Gangadharan Murugusundaramoorthy, Basem Aref Frasin, Tariq Al-Hawary (2022)

Mathematica Bohemica

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The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes ${𝒮𝒫}_{p} (α, β)$ and ${𝒰𝒞𝒱}_{p} (α, β)$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

On the Lukacs property for free random variables

Kamil Szpojankowski (2015)

Studia Mathematica

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The Lukacs property of the free Poisson distribution is studied. We prove that if free and are free Poisson distributed with suitable parameters, then + and ${(+)}^{- 1 / 2} {(+)}^{- 1 / 2}$ are free. As an auxiliary result we compute the joint cumulants of and $^{- 1}$ for free Poisson distributed . We also study the Lukacs property of the free Gamma distribution.

Existence of solutions to the Poisson equation in $L_{p}$ -weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_{p}$ , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.

Canonical Poisson-Nijenhuis structures on higher order tangent bundles

P. M. Kouotchop Wamba (2014)

Annales Polonici Mathematici

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Let M be a smooth manifold of dimension m>0, and denote by $S_{c a n}$ the canonical Nijenhuis tensor on TM. Let Π be a Poisson bivector on M and $Π^{T}$ the complete lift of Π on TM. In a previous paper, we have shown that $(T M, Π^{T}, S_{c a n})$ is a Poisson-Nijenhuis manifold. Recently, the higher order tangent lifts of Poisson manifolds from M to $T^{r} M$ have been studied and some properties were given. Furthermore, the canonical Nijenhuis tensors on $T^{A} M$ are described by A. Cabras and I. Kolář [Arch. Math. (Brno) 38 (2002),...

On a deformed version of the two-disk dynamo system

Cristian Lăzureanu, Camelia Petrişor, Ciprian Hedrea (2021)

Applications of Mathematics

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We give some deformations of the Rikitake two-disk dynamo system. Particularly, we consider an integrable deformation of an integrable version of the Rikitake system. The deformed system is a three-dimensional Hamilton-Poisson system. We present two Lie-Poisson structures and also symplectic realizations. Furthermore, we give a prequantization result of one of the Poisson manifold. We study the stability of the equilibrium states and we prove the existence of periodic orbits. We analyze...

Prolongation of Poisson $2$ -form on Weil bundles

Norbert Mahoungou Moukala, Basile Guy Richard Bossoto (2016)

Archivum Mathematicum

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In this paper, $M$ denotes a smooth manifold of dimension $n$ , $A$ a Weil algebra and $M^{A}$ the associated Weil bundle. When $(M, ω_{M})$ is a Poisson manifold with $2$ -form $ω_{M}$ , we construct the $2$ -Poisson form $ω_{M^{A}}^{A}$ , prolongation on $M^{A}$ of the $2$ -Poisson form $ω_{M}$ . We give a necessary and sufficient condition for that $M^{A}$ be an $A$ -Poisson manifold.

GCD sums from Poisson integrals and systems of dilated functions

Christoph Aistleitner, István Berkes, Kristian Seip (2015)

Journal of the European Mathematical Society

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Upper bounds for GCD sums of the form $\sum_{k, ℓ = 1}^{N} \frac{{(\gcd (n_{k}, n_{ℓ}))}^{2 α}}{{(n_{k} n_{ℓ})}^{α}}$ are established, where ${(n_{k})}_{1 \leq k \leq N}$ is any sequence of distinct positive integers and $0 < α \leq 1$ ; the estimate for $α = 1 / 2$ solves in particular a problem of Dyer and Harman from 1986, and the estimates are optimal except possibly for $α = 1 / 2$ . The method of proof is based on identifying the sum as a certain Poisson integral on a polydisc; as a byproduct, estimates for the largest eigenvalues of the associated GCD matrices are also found. The bounds for such GCD sums are used to...

Real and complex analytic sets. The relevance of Segre varieties

Klas Diederich, Emmanuel Mazzilli (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X \subset {ℂ^{n}}^{n}$ be a closed real-analytic subset and put $𝒜 : = {z \in X ∣ \exists A \subset X, germ of a complex-analytic set, z \in A, {dim}_{z} A > 0}$ This article deals with the question of the structure of $𝒜$ . In the main result a natural proof is given for the fact, that $𝒜$ always is closed. As a main tool an interesting relation between complex analytic subsets of $X$ of positive dimension and the Segre varieties of $X$ is proved and exploited.