The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Wasserstein metric and subordination”

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 ( 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.

Convolution operators with anisotropically homogeneous measures on 2 n with n-dimensional support

E. Ferreyra, T. Godoy, M. Urciuolo (2002)

Colloquium Mathematicae

Similarity:

Let α i , β i > 0 , 1 ≤ i ≤ n, and for t > 0 and x = (x₁,...,xₙ) ∈ ℝⁿ, let t x = ( t α x , . . . , t α x ) , t x = ( t β x , . . . , t β x ) and | | x | | = i = 1 n | x i | 1 / α i . Let φ₁,...,φₙ be real functions in C ( - 0 ) such that φ = (φ₁,..., φₙ) satisfies φ(t • x) = t ∘ φ(x). Let γ > 0 and let μ be the Borel measure on 2 n given by μ ( E ) = χ E ( x , φ ( x ) ) | | x | | γ - α d x , where α = i = 1 n α i and dx denotes the Lebesgue measure on ℝⁿ. Let T μ f = μ f and let | | T μ | | p , q be the operator norm of T μ from L p ( 2 n ) into L q ( 2 n ) , where the L p spaces are taken with respect to the Lebesgue measure. The type set E μ is defined by E μ = ( 1 / p , 1 / q ) : | | T μ | | p , q < , 1 p , q . In the case α i β k for 1 ≤ i,k ≤ n we characterize the...

On almost everywhere differentiability of the metric projection on closed sets in l p ( n ) , 2 < p <

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

Similarity:

Let F be a closed subset of n and let P ( x ) denote the metric projection (closest point mapping) of x n onto F in l p -norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in n in the Euclidean case p = 2 . We consider the case 2 < p < and prove that the i th component P i ( x ) of P ( x ) is differentiable a.e. if P i ( x ) x i and satisfies Hölder condition of order 1 / ( p - 1 ) if P i ( x ) = x i .

Measure-geometric Laplacians for partially atomic measures

Marc Kesseböhmer, Tony Samuel, Hendrik Weyer (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure η supported on a compact subset of U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator η and a second order differential operator Δ η , with respect to η . We generalize this approach to measures of the form η : = ν + δ , where ν is non-atomic and δ is finitely supported. We determine...

On inhomogeneous self-similar measures and their L q spectra

Przemysław Liszka (2013)

Annales Polonici Mathematici

Similarity:

Let S i : d d for i = 1,..., N be contracting similarities, let ( p , . . . , p N , p ) be a probability vector and let ν be a probability measure on d with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on d such that μ = i = 1 N p i μ 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 ( 1 , ) . 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...

L p -improving properties of certain singular measures on the Heisenberg group

Pablo Rocha (2022)

Mathematica Bohemica

Similarity:

Let μ A be the singular measure on the Heisenberg group n supported on the graph of the quadratic function ϕ ( y ) = y t A y , where A is a 2 n × 2 n real symmetric matrix. If det ( 2 A ± J ) 0 , we prove that the operator of convolution by μ A on the right is bounded from L ( 2 n + 2 ) ( 2 n + 1 ) ( n ) to L 2 n + 2 ( n ) . We also study the type set of the measures d ν γ ( y , s ) = η ( y ) | y | - γ d μ A ( y , s ) , for 0 γ < 2 n , where η is a cut-off function around the origin on 2 n . Moreover, for γ = 0 we characterize the type set of ν 0 .

Generalized Lebesgue points for Sobolev functions

Nijjwal Karak (2017)

Czechoslovak Mathematical Journal

Similarity:

In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point x in a metric measure space ( X , d , μ ) is called a generalized Lebesgue point of a measurable function f if the medians of f over the balls B ( x , r ) converge to f ( x ) when r converges to 0 . We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function....

On the characterization of harmonic functions with initial data in Morrey space

Bo Li, Jinxia Li, Bolin Ma, Tianjun Shen (2024)

Czechoslovak Mathematical Journal

Similarity:

Let ( X , d , μ ) be a metric measure space satisfying the doubling condition and an L 2 -Poincaré inequality. Consider the nonnegative operator generalized by a Dirichlet form on X . We will show that a solution u to ( - t 2 + ) u = 0 on X × + satisfies an α -Carleson condition if and only if u can be represented as the Poisson integral of the operator with the trace in the generalized Morrey space L 2 , α ( X ) , where α is a nonnegative function defined on a class of balls in X . This result extends the analogous characterization...

Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps

Viviane Baladi, Daniel Smania (2012)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We consider C 2 families t f t of  C 4 unimodal maps f t whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure μ t of  f t depends differentiably on  t , as a distribution of order 1 . The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of  μ t for a Benedicks-Carleson map f t , in terms of a single smooth function and the...

Induced mappings on hyperspaces F n K ( X )

Enrique Castañeda-Alvarado, Roberto C. Mondragón-Alvarez, Norberto Ordoñez (2024)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Given a metric continuum X and a positive integer n , F n ( X ) denotes the hyperspace of all nonempty subsets of X with at most n points endowed with the Hausdorff metric. For K F n ( X ) , F n ( K , X ) denotes the set of elements of F n ( X ) containing K and F n K ( X ) denotes the quotient space obtained from F n ( X ) by shrinking F n ( K , X ) to one point set. Given a map f : X Y between continua, f n : F n ( X ) F n ( Y ) denotes the induced map defined by f n ( A ) = f ( A ) . Let K F n ( X ) , we shall consider the induced map in the natural way f n , K : F n K ( X ) F n f ( K ) ( Y ) . In this paper we consider the maps f , f n , f n , K for some...

Remarks on WDC sets

Dušan Pokorný, Luděk Zajíček (2021)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results concern WDC sets A 2 . We prove that, for such A , the distance function d A = dist ( · , A ) is a “DC aura” for A , which implies that each closed locally WDC set in 2 is a WDC set. Another consequence is that compact WDC subsets of 2 form a Borel subset of the space of all compact sets.

About w c s -covers and w c s * -networks on the Vietoris hyperspace ( X )

Luong Quoc Tuyen, Ong V. Tuyen, Phan D. Tuan, Nguzen X. Truc (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study some generalized metric properties on the hyperspace ( X ) of finite subsets of a space X endowed with the Vietoris topology. We prove that X has a point-star network consisting of (countable) w c s -covers if and only if so does ( X ) . Moreover, X has a sequence of w c s -covers with property ( P ) which is a point-star network if and only if so does ( X ) , where ( P ) is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable....