In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [6] in order to remove mixed Poisson-Gaussian (MPG) noise. existing splitting algorithm TV-IC, an inner loop by Newton method had be adopted one nonlinear optimization subproblem, which increased computation cost per outer loop. By introducing a bilinear constraint a...

There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to more general class of phase functions. The main methods Bourgain-Demeter's $l^2$ decoupling theorem induction on scales. second prove positive maximal extension operator hypersurfaces with principal curvatures. sharp $L^2$ estimates Du Zhang, bilinear method Wolff Tao.

We represent a bilinear Calder\'on-Zygmund operator at given smoothness level as finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in sparse $T(1)$-type bound, which turn yields directly new sharp weighted estimates on Lebesgue Sobolev spaces. Moreover, we apply the theorem to study fractional dif...

While an integration by parts formula for the bilinear form of hypersingular boundary integral operator transient heat equation in three spatial dimensions is available literature, a proof this seems to be missing. Moreover, contains term including time derivative fundamental solution equation, whose interpretation difficult at second glance. To fill these gaps, we provide rigorous general vers...

In this paper, first we show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphism between adjoint representation and coadjoint representation. Then introduce notions of relative Rota-Baxter operators on algebras pre-Lie-Yamaguti algebras. We prove gives rise to naturally operator algebra. Finally, study symplectic structures algebra, which give as well As ...

The paper is concerned with compact bilinear operators on asymmetric normed spaces. study of multilinear spaces was initiated by Latreche and Dahia (2020) [24]. We go further in this direction prove a Schauder type theorem the compactness adjoint operator ideal properties operators. These extend some results Ramanujan Schock (1985) [34], Ruch (1989) [36], Banach On space forms one introduces an...

Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...

Abstract We consider an additive Vanka‐type smoother for the Poisson equation discretized by standard finite difference centered scheme. Using local Fourier analysis, we derive analytical formulas optimal smoothing factors vertex‐wise and element‐wise Vanka smoothers. In one dimension is equivalent to scaled mass operator obtained from linear element method in two dimensions bilinear plus a ide...

We extend the abstract frameworks for the multigrid analysis for nonconforming finite elements to the case where the assumptions of the second Strang lemma are violated. The consistency error is studied in detail for finite element discretizations on domains with curved boundaries. This is applied to prove the approximation property for conforming elements, stabilized Q1/P0elements, and nonconf...