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我们将介绍由Bar-Gauduchon-Moroianu给出的spin流形上Dirac算子在度量变化时一阶变分公式的证明。作为应用,我们将计算Dirac算子沿Ricci flow的一阶变分。
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators l_r M^r+?+l_1 M+l_0 where l_0,…,l_r are polynomials in x and Mx=x^b M for some...
We introduced a new family of translation invariant geometric measures arising from Integral Geometry of convex bodies. These measures are related to a family of new Monge-Ampère type operators conver...
The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-lo...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
In this digital world, there is a large requirement of high resolution satellite image. Images at a low resolution may contain relevant information that has to be integrated with the high resolution i...
Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators i...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
GIAMBELLI, PIERI, AND TABLEAU FORMULAS VIA RAISING OPERATORS     GIAMBELLI  PIERI  TABLEAU FORMULAS       font style='font-size:12px;'> 2015/12/17
We give a direct proof of the equivalence between the Giambelli and Pieri type formulas for Hall-Littlewood functions using Young’s raising operators, parallel to joint work with Buch and Kresch for ...
We use the theory of Gabor frames to prove the boundedness of bilinear pseudodifferentialoperators on products of modulation spaces. In particular,we show that bilinear pseudodifferential operators co...
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the opera...
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W . We construct a one parameter family of flat connections ∇κ on h with values in any finite–dimensional g–moduleV...
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
Transition operators on co-compact G-spaces     co-compact G-spaces  Transition operator       font style='font-size:12px;'> 2015/8/26
We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with ...

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