Results 1 to 10 of about 6,026 (265)

A pointwise estimate for pseudo-differential operators

Bulletin of Mathematical Sciences, 2023
Let [Formula: see text] be a pseudo-differential operator defined by the symbol [Formula: see text] with [Formula: see text] [Formula: see text]. It is shown that if [Formula: see text], then the operator satisfies the following pointwise estimate: (Tau)♯
Guangqing Wang, Wenyi Chen
doaj   +1 more source

On L 2 $L^{2}$ -boundedness of Fourier integral operators

Journal of Inequalities and Applications, 2020
Let T a , φ $T_{a,\varphi }$ be a Fourier integral operator with symbol a and phase φ. In this paper, under the conditions a ( x , ξ ) ∈ L ∞ S ρ n ( ρ − 1 ) / 2 ( ω ) $a(x,\xi )\in L^{\infty }S^{n(\rho -1)/2}_{\rho }(\omega )$ and φ ∈ L ∞ Φ 2 $\varphi ...
Jie Yang, Wenyi Chen, Jiang Zhou
doaj   +1 more source

Application of the Littlewood-Paley method to Calderon-Zygmund operators [PDF]

Surveys in Mathematics and its Applications, 2022
In this article, we establish the conditions for the pseudo-differential operator T under which this operator can be represented in convolution form with the singular kernel that satisfies |∂ xα ∂ zβ k(x,z)| ≤ Aβα(L)|z|-l-m-|β |-L for all z ≠ 0, and all ...
Mykola Yaremenko
doaj  

Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

Journal of Inequalities and Applications, 2009
We study the existence and uniqueness of almost automorphic (resp., pseudo-almost automorphic) solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain.
Bruno de Andrade, Claudio Cuevas
doaj   +2 more sources

Pseudo-differential operators and equations in a discrete half-space

Mathematical Modelling and Analysis, 2018
We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space.
Alexander V. Vasilyev, Vladimir B. Vasilyev   +1 more
doaj   +1 more source

Properties of single layer potentials for a pseudo- differential equation related to a linear transformation of a rotationally invariant stable stochastic process

Математичні Студії, 2021
This article is aimed at determining existence conditions of single layer potentials for pseudo-differential equations related to some linear transformations of a rotationally invariant stable stochastic process in a multidimensional Euclidean space and ...
Kh. V. Mamalyha, M. M. Osypchuk
doaj   +1 more source

On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations

Karpatsʹkì Matematičnì Publìkacìï, 2015
A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a
M.M. Osypchuk
doaj   +1 more source

On single-layer potentials for a class of pseudo-differential equations related to linear transformations of a symmetric $\alpha$-stable stochastic process

Karpatsʹkì Matematičnì Publìkacìï, 2019
In this article an arbitrary invertible linear transformations of a symmetric $\alpha$-stable stochastic process in $d$-dimensional Euclidean space $\mathbb{R}^d$ are investigated.
Kh.V. Mamalyha, M.M. Osypchuk
doaj   +1 more source

A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics, 2020
A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator ...
Benjamin Akers, Tony Liu, Jonah Reeger
doaj   +1 more source

Asymptotic Consideration of Rayleigh Waves on a Coated Orthorhombic Elastic Half-Space Reinforced Using an Elastic Winkler Foundation

Mathematical and Computational Applications, 2023
This article derives approximate formulations for Rayleigh waves on a coated orthorhombic elastic half-space with a prescribed vertical load acting as an elastic Winkler foundation.
Ali M. Mubaraki
doaj   +1 more source