Results 31 to 40 of about 2,392,144 (197)

On the Riesz Transforms for Gaussian Measures

Journal of Functional Analysis, 1994
Let \(B\) be an \(n\times n\) positive-definite symmetric matrix, and \(L_ B\) the second order partial differential operator in \(\mathbb{R}^ n\) defined by \(L_ Bu= {1\over 2}\Delta- Bx\cdot \nabla u\). The operator \(L_ B\) is selfadjoint with respect to the Gaussian probability measure \(\gamma_ n^ B(x)dx\), where \(\gamma_ n^ B(x)= C_{n,B} \exp ...
openaire   +2 more sources

Fractional Moment Theory for Anomalous Transport: A Unified Framework for Lévy Flights, Fractals, and Complex Dynamical Systems

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 14964-15009, 15 September 2026.
ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley   +1 more source

Potential theory of signed Riesz Kernels: capacity and Hausdorff measure [PDF]

, 2004
In this paper, we study the natural capacity γα related to the Riesz kernels x/∣x∣1 + α in ℝn, where 0 < α < n. For noninteger α, an unexpected behaviour arises: for 0 < α < 1, compact sets in ℝn with finite α-Hausdorff measure have zero γα capacity.
Prat, Laura
core   +1 more source

A new perspective on the Riesz potential

Advances in Nonlinear Analysis, 2017
This paper offers a new perspective to look at the Riesz potential. On the one hand, it is shown that not only 𝔏q,q⁢p-1⁢(n-α⁢p)∩𝔏p,κ-α⁢p\mathfrak{L}^{q,qp^{-1}(n-\alpha p)}\cap\mathfrak{L}^{p,\kappa-\alpha p} contains Iα⁢Lp,κ{I_{\alpha}L^{p,\kappa ...
Xiao Jie
doaj   +1 more source

The precise representative for the gradient of the Riesz potential of a finite measure

Journal of the London Mathematical Society, 2022
Given a finite nonnegative Borel measure $m$ in $\mathbb{R}^{d}$, we identify the Lebesgue set $\mathcal{L}(V_{s}) \subset \mathbb{R}^{d}$ of the vector-valued function $$V_{s}(x) = \int_{\mathbb{R}^{d}}\frac{x - y}{|x - y|^{s + 1}} \mathrm{d}m(y), $$ for any order $0 < s < d$.
Cufí, Julià, Ponce, Augusto C., Verdera, Joan   +2 more
openaire   +3 more sources

Amenability Constants for Unconditional Sums of Banach Algebras

Mathematische Nachrichten, Volume 299, Issue 9, Page 2472-2494, September 2026.
ABSTRACT We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family (Ai)i∈I$(A_i)_{i\in I}$ of Banach algebras and a Banach sequence lattice E$E$ on I$I$, the E$E$‐sum ⨁i∈IAiE${\bigl (\bigoplus _{i\in I} A_i\bigr)}_{\!E}$ carries a natural Banach algebra structure via coordinatewise multiplication.
Tomasz Kania, Jerzy Ka̧kol
wiley   +1 more source

A Semi‐Discrete Lagrangian‐Eulerian Numerical Scheme for Diffusive‐Dispersive Conservation Laws With Discontinuous Coefficient

Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.
ABSTRACT In this work, we present an extension of the semi‐discrete Lagrangian‐Eulerian numerical scheme for diffusive‐dispersive conservation law problems, including a jump discontinuous flux function. As in the one‐dimensional scalar hyperbolic case, the no‐flow curves also organize the geometry of the method.
Eduardo Abreu, Wanderson Lambert, Erivaldo Lima   +2 more
wiley   +1 more source

Boundedness of Bessel–Riesz Operator in Variable Lebesgue Measure Spaces

Mathematics
In this manuscript, we establish the boundedness of the Bessel–Riesz operator Iα,γf in variable Lebesgue spaces Lp(·). We prove that Iα,γf is bounded from Lp(·) to Lp(·) and from Lp(·) to Lq(·).
Muhammad Nasir, Ali Raza, Luminiţa-Ioana Cotîrlă, Daniel Breaz   +3 more
doaj   +1 more source

Points of narrowness and uniformly narrow operators

Karpatsʹkì Matematičnì Publìkacìï, 2017
It is known that the sum of every two narrow operators on $L_1$ is narrow, however the same is false for $L_p$ with $1 < p < \infty$. The present paper continues numerous investigations of the kind.
A.I. Gumenchuk, I.V. Krasikova, M.M. Popov   +2 more
doaj   +1 more source

Improving the Finite Sample Estimation of Average Treatment Effects Using Double/Debiased Machine Learning With Propensity Score Calibration

Journal of Applied Econometrics, Volume 41, Issue 5, Page 613-626, August 2026.
ABSTRACT Double/debiased machine learning (DML) uses for estimating an average treatment effect (ATE) a double‐robust score function that relies on the prediction of nuisance functions, such as the propensity score, which is the probability of treatment assignment given covariates.
Daniele Ballinari, Nora Bearth
wiley   +1 more source