Operator semistable probability measures on $R^N$

A. Łuczak

Displaying similar documents to “Operator semistable probability measures on $R^{N}$ ”

Corrigenda to “Operator semi-stable probability measures on $R^{N}$ ”

A. Luczak (1987)

Colloquium Mathematicae

Similarity:

Self-decomposable probability distributions on $R^{m}$

Kazimierz Urbanik (1969)

Applicationes Mathematicae

Similarity:

On the isotropic constant of marginals

Grigoris Paouris (2012)

Studia Mathematica

Similarity:

We show that if μ₁, ..., μₘ are log-concave subgaussian or supergaussian probability measures in $ℝ^{n_{i}}$ , i ≤ m, then for every F in the Grassmannian $G_{N, n}$ , where N = n₁ + ⋯ + nₘ and n< N, the isotropic constant of the marginal of the product of these measures, $π_{F} (μ ₁ \otimes \dots \otimes μ ₘ)$ , is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.

Limit theorems for random fields

Nguyen van Thu

Similarity:

CONTENTSIntroduction............................................................................................................................................................................ 51. Notation and preliminaries............................................................................................................................................ 52. Statement of the problem..................................................................................................................................................

Stable solutions of $- Δ u = f (u)$ in $ℝ^{N}$

Louis Dupaigne, Alberto Farina (2010)

Journal of the European Mathematical Society

Similarity:

Several Liouville-type theorems are presented for stable solutions of the equation $- Δ u = f (u)$ in $ℝ^{N}$ , where $f > 0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

On inhomogeneous self-similar measures and their $L^{q}$ spectra

Przemysław Liszka (2013)

Annales Polonici Mathematici

Similarity:

Let $S_{i} : ℝ^{d} \to ℝ^{d}$ for i = 1,..., N be contracting similarities, let $(p ₁, . . ., p_{N}, p)$ be a probability vector and let ν be a probability measure on $ℝ^{d}$ with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on $ℝ^{d}$ such that $μ = \sum_{i = 1}^{N} p_{i} μ \circ S_{i}^{- 1} + p ν$ . We give satisfactory estimates for the lower and upper bounds of the $L^{q}$ spectra of inhomogeneous self-similar measures. The case in which there are a countable number of contracting similarities and probabilities is considered. In particular,...

On the duality between $p$ -modulus and probability measures

Luigi Ambrosio, Simone Di Marino, Giuseppe Savaré (2015)

Journal of the European Mathematical Society

Similarity:

Motivated by recent developments on calculus in metric measure spaces $(X, d, m)$ , we prove a general duality principle between Fuglede’s notion [15] of $p$ -modulus for families of finite Borel measures in $(X, d)$ and probability measures with barycenter in $L^{q} (X, m)$ , with $q$ dual exponent of $p \in (1, \infty)$ . We apply this general duality principle to study null sets for families of parametric and non-parametric curves in $X$ . In the final part of the paper we provide a new proof, independent of optimal transportation, of the...

A descent map for curves with totally degenerate semi-stable reduction

Shahed Sharif (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $K$ be a local field of residue characteristic $p$ . Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- $p$ rational torsion subgroup on the Jacobian of $C$ . We also determine divisibility of line bundles on $C$ , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of $C$ .

Wasserstein metric and subordination

Philippe Clément, Wolfgang Desch (2008)

Studia Mathematica

Similarity:

Let $(X, d_{X})$ , $(Ω, d_{Ω})$ be complete separable metric spaces. Denote by (X) the space of probability measures on X, by $W_{p}$ the p-Wasserstein metric with some p ∈ [1,∞), and by $_{p} (X)$ the space of probability measures on X with finite Wasserstein distance from any point measure. Let $f : Ω \to_{p} (X)$ , $ω \mapsto f_{ω}$ , be a Borel map such that f is a contraction from $(Ω, d_{Ω})$ into $(_{p} (X), W_{p})$ . Let ν₁,ν₂ be probability measures on Ω with $W_{p} (ν ₁, ν ₂)$ finite. On X we consider the subordinated measures $μ_{i} = \int_{Ω} f_{ω} d ν_{i} (ω)$ . Then $W_{p} (μ ₁, μ ₂) \leq W_{p} (ν ₁, ν ₂)$ . As an application we show that the solution measures $ϱ_{α} (t)$ ...

Spaces of functions on domain $Ω$ , whose $k$ -th derivatives are measures defined on $\bar{Ω}$

Jiří Souček (1972)

Časopis pro pěstování matematiky

Similarity:

On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag (2010)

Journal of the European Mathematical Society

Similarity:

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.

A Local Limit Theorem on the Semi-Direct Product of $ℝ^{* +}$ and $ℝ^{d}$

Emile Le Page, Marc Peigne (1994)

Publications mathématiques et informatique de Rennes

Similarity:

Osgood type conditions for an m th-order differential equation

Stanisaw Szufla (1998)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

We present a new theorem on the differential inequality $u^{(m)} \leq w (u)$ . Next, we apply this result to obtain existence theorems for the equation $x^{(m)} = f (t, x)$ .

On NIP and invariant measures

Ehud Hrushovski, Anand Pillay (2011)

Journal of the European Mathematical Society

Similarity:

We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if $p = tp (b / A)$ does not fork over $A$ then the Lascar strong type of $b$ over $A$ coincides with the compact strong type of $b$ over $A$ and any global nonforking extension of $p$ is Borel definable over $bdd (A)$ , (ii) analogous statements for Keisler measures and definable groups, including the fact that $G^{000} = G^{00}$ for $G$ ...

Convergence to stable laws and a local limit theorem for stochastic recursions

Mariusz Mirek (2010)

Colloquium Mathematicae

Similarity:

We consider the random recursion $X ₙ^{x} = M ₙ X_{n - 1}^{x} + Q ₙ + N ₙ (X_{n - 1}^{x})$ , where x ∈ ℝ and (Mₙ,Qₙ,Nₙ) are i.i.d., Qₙ has a heavy tail with exponent α > 0, the tail of Mₙ is lighter and $N ₙ (X_{n - 1}^{x})$ is smaller at infinity, than $M ₙ X_{n - 1}^{x}$ . Using the asymptotics of the stationary solutions we show that properly normalized Birkhoff sums $S ₙ^{x} = \sum_{k = 0}^{n} X_{k}^{x}$ converge weakly to an α-stable law for α ∈ (0,2]. The related local limit theorem is also proved.

$L^{p}$ -improving properties of measures of positive energy dimension

Kathryn E. Hare, Maria Roginskaya (2005)

Colloquium Mathematicae

Similarity:

A measure is called $L^{p}$ -improving if it acts by convolution as a bounded operator from $L^{p}$ to $L^{q}$ for some q > p. Positive measures which are $L^{p}$ -improving are known to have positive Hausdorff dimension. We extend this result to complex $L^{p}$ -improving measures and show that even their energy dimension is positive. Measures of positive energy dimension are seen to be the Lipschitz measures and are characterized in terms of their improving behaviour on a subset of $L^{p}$ -functions.

On $(n, m)$ - $A$ -normal and $(n, m)$ - $A$ -quasinormal semi-Hilbertian space operators

Samir Al Mohammady, Sid Ahmed Ould Beinane, Sid Ahmed Ould Ahmed Mahmoud (2022)

Mathematica Bohemica

Similarity:

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let $ℋ$ be a Hilbert space and let $A$ be a positive bounded operator on $ℋ$ . The semi-inner product ${〈 h ∣ k 〉}_{A} : = 〈 A h ∣ k 〉$ , $h, k \in ℋ$ , induces a semi-norm ${∥ \cdot ∥}_{A}$ . This makes $ℋ$ into a semi-Hilbertian space. An operator $T \in ℬ_{A} (ℋ)$ is said to be $(n, m)$ - $A$ -normal if $[T^{n}, {(T^{♯_{A}})}^{m}] : = T^{n} {(T^{♯_{A}})}^{m} - {(T^{♯_{A}})}^{m} T^{n} = 0$ for some positive integers $n$ and $m$ .

Integral representation and relaxation for functionals defined on measures

Ennio De Giorgi, Luigi Ambrosio, Giuseppe Buttazzo (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Given a separable metric locally compact space $\Omega$ , and a positive finite non-atomic measure $\lambda$ on $\Omega$ , we study the integral representation on the space of measures with bounded variation $\Omega$ of the lower semicontinuous envelope of the functional $F(u)=\int_{\Omega}f(x,u)d\lambda\qquad u\in L^{1}(\Omega,\lambda,\mathbb{R}^{n})$ with respect to the weak convergence of measures.

Self-affine measures that are $L^{p}$ -improving

Kathryn E. Hare (2015)

Colloquium Mathematicae

Similarity:

A measure is called $L^{p}$ -improving if it acts by convolution as a bounded operator from $L^{q}$ to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are $L^{p}$ -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be $L^{p}$ -improving.

Some properties of the topology of $α$ -sets

D. Andrijević (1984)

Matematički Vesnik

Similarity:

On biorthogonal systems whose functionals are finitely supported

Christina Brech, Piotr Koszmider (2011)

Fundamenta Mathematicae

Similarity:

We show that for each natural number n > 1, it is consistent that there is a compact Hausdorff totally disconnected space $K_{2 n}$ such that $C (K_{2 n})$ has no uncountable (semi)biorthogonal sequence ${(f_{ξ}, μ_{ξ})}_{ξ \in ω ₁}$ where $μ_{ξ}$ ’s are atomic measures with supports consisting of at most 2n-1 points of $K_{2 n}$ , but has biorthogonal systems ${(f_{ξ}, μ_{ξ})}_{ξ \in ω ₁}$ where $μ_{ξ}$ ’s are atomic measures with supports consisting of 2n points. This complements a result of Todorcevic which implies that it is consistent that such spaces do not exist: he proves...

Continuous linear functionals on the space of Borel vector measures

Pola Siwek (2008)

Annales Polonici Mathematici

Similarity:

We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm ${| | \cdot | |}_{ℱ}$ and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space $(ℳ, | | \cdot | |_{ℱ}) *$ is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals...

Displaying similar documents to “Operator semistable probability measures on R N ”

Displaying similar documents to “Operator semistable probability measures on $R^{N}$ ”