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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Bourguignon-Gauduchon's variation formula for Dirac operators
Dirac算子 Bourguignon-Gauduchon 变分公式
2023/11/13
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。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：ENERGY, POINTWISE, AND FREE BOUNDARY APPROXIMATION OF THE OBSTACLE PROBLEM FOR NONLOCAL OPERATORS
非局部 算子障碍物 自由边界 近似
2023/4/28
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...
CONFORMAL INVARIANTS ASSOCIATED TO A MEASURE: CONFORMALLY COVARIANT OPERATORS
CONFORMAL INVARIANTS ASSOCIATED MEASURE CONFORMALLY COVARIANT OPERATORS
2014/4/3
In this paper we study Riemannian manifolds (Mn, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling...
Real-Variable Theory and Fourier Integral Operators on Semisimple Lie Groups and Symmetric Spaces of Real Rank One
Real-Variable Theory Fourier Integral Operators Semisimple Lie Groups Symmetric Spaces Real Rank One
2014/4/3
Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will p...
NONLINEAR MAXIMUM PRINCIPLES FOR DISSIPATIVE LINEAR NONLOCAL OPERATORS AND APPLICATIONS
NONLINEAR MAXIMUM PRINCIPLES DISSIPATIVE LINEAR NONLOCAL OPERATORS APPLICATIONS
2014/4/3
We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators,that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of glo...
Estimates for approximation numbers of some classes of composition operators on the Hardy space
approximation numbers Blaschke product composition operator cusp map Hardy space modulus of continuity Schatten classes
2012/6/21
We give estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approxim...
On the power-bounded operators of classes $C_{0 \cdot}$ and $C_{1 \cdot}$
power-bounded operators C0 operators strongly stable operators Functional Analysis
2012/6/19
By a bounded backward sequence of the operator $T$ we mean a bounded sequence $\{x_n\}$ satisfying $Tx_{n+1}=x_n$. In \cite{Pa} we have characterized contractions with strongly stable nonunitary part ...
Weighted Lipschitz estiamtes for commutators of one-sided operators on one-sided Triebel-Lizorkin spaces
one-sided weight weighted Lipschitz function one-sided Triebel-Lizorkin space one-sided singular integral
2012/6/15
Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spa...
Interpolation of bilinear operators and compactness
interpolation Banach spaces bilinear operators compactness
2012/6/6
The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's com...
Hypercyclic operators on countably dimensional spaces
Cyclic operators hypercyclic operators invariant subspaces topological vector spaces
2012/5/25
According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\Sigma(X)$ of countable dense linearly indepen...
On Self-Adjointness Of 1-D Schrodinger Operators With $δ$-Interactions
Schrodinger operator local point interaction self-adjoint operator deficiency indices Jacobi matrices
2012/4/23
In the present work we consider in $L^2(\mathbb{R}_+)$ the Schr\"odinger operator $\mathrm{H_{X,\alpha}}=-\mathrm{\frac{d^2}{dx^2}}+\sum_{n=1}^{\infty}\alpha_n\delta(x-x_n)$. We investigate and comple...
Products of Unbounded Normal Operators
Product of operators Normal hyponormal subnormal operators
2012/2/29
The present paper partly constitutes an "unbounded" follow-up of a paper by I. Kaplansky dealing with bounded products of normal operators. Results on the normality of unbounded products are also incl...
More on the Normality of the Unbounded Product of Two Normal Operators
Unbounded operators. Selfadjoint and normal operators. Operator products
2012/2/29
Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give conditions making their product normal. This is a continuation of recently obtained results on this subject.
Hardy Spaces $H_L^p({\mathbb R}^n)$ Associated to Operators Satisfying $k$-Davies-Gaffney Estimates
Hardy space Hardy-Sobolev space k-Davies-Gaffney estimate Schrodinger type operator
2011/9/21
Abstract: Let $L$ be a one to one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the a...
Pseudodifferential operators on periodic graphs
Pseudodifferential operators periodic graphs Functional Analysis
2011/9/21
Abstract: The main aim of the paper is Fredholm properties of a class of bounded linear operators acting on weighted Lebesgue spaces on an infinite metric graph $\Gamma$ which is periodic with respect...