A theoretical framework for proposed \weak Tau" type of approximation schemes is considered in the context of least-squares parameter estimation problems for partial dierential equations. A convergence theory which includes parameter estimate convergence and method stability is developed. Numerical results demonstrating the possible advantages of these ideas are also presented.

This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg (·), Proxg (B) = argmin X m ∑

We construct a strictly singular non-compact operator on Gowers’ and Maurey’s space GM .

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg (·), Proxg (B) = argmin X m ∑

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

We study the self-duality operator on conic 4-manifolds. The self-duality operator can be identified as a regular singular operator in the sense of Brüning and Seeley, based on which we construct its parametrizations and closed extensions. We also compute the indexes.

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel–Lizorkin spaces respectively.