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Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications

Le Mau HaiNguyen Xuan Hong — 2014

Annales Polonici Mathematici

The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge-Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in C n - 1 -capacity then the sequence of the Monge-Ampère measures of subextensions is weakly*-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.

Generalized Morrey spaces associated to Schrödinger operators and applications

Nguyen Ngoc TrongLe Xuan Truong — 2018

Czechoslovak Mathematical Journal

We first introduce new weighted Morrey spaces related to certain non-negative potentials satisfying the reverse Hölder inequality. Then we establish the weighted strong-type and weak-type estimates for the Riesz transforms and fractional integrals associated to Schrödinger operators. As an application, we prove the Calderón-Zygmund estimates for solutions to Schrödinger equation on these new spaces. Our results cover a number of known results.

On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms

Nguyen Thanh HongTrinh TuanNguyen Xuan Thao — 2013

Applications of Mathematics

We deal with several classes of integral transformations of the form f ( x ) D + 2 1 u ( e - u cosh ( x + v ) + e - u cosh ( x - v ) ) h ( u ) f ( v ) d u d v , where D is an operator. In case D is the identity operator, we obtain several operator properties on L p ( + ) with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on L 2 ( + ) and define the inversion formula. Further, for an other class of differential operators of finite...

Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation

S. NatarajanA.J.M. FerreiraHung Nguyen-Xuan — 2014

Curved and Layered Structures

In this paper, we study the static bending and free vibration of cross-ply laminated composite plates using sinusoidal deformation theory. The plate kinematics is based on the recently proposed Carrera Unified Formulation (CUF), and the field variables are discretized with the non-uniform rational B-splines within the framework of isogeometric analysis (IGA). The proposed approach allows the construction of higher-order smooth functions with less computational effort.Moreover, within the framework...

More on the Kechris-Pestov-Todorcevic correspondence: Precompact expansions

L. Nguyen Van Thé — 2013

Fundamenta Mathematicae

In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...

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