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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/17
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/23
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Non-local operators with low-order singular kernels
低阶 奇异内核 非局部 运算符 正则性估计 二阶椭圆方程
2023/4/24
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...
FAST DIRECTIONAL MULTILEVEL ALGORITHMS FOR OSCILLATORY KERNELS
N-body problems scattering problems Helmholtz equation oscillatory kernels fast multipole methods separated representations random sampling operator compression multidirectional computation multiscale methods
2015/7/14
This paper introduces a new directional multilevel algorithm for solving N-body orN-point problems with highly oscillatory kernels. These systems often result from the boundary integral formulations o...
Resummed memory kernels in generalized system-bath master equations
Langevin equation Perturbation theory Molecular dynamicsPopulation dynamics Matrix equations
2014/8/21
Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the ...
Semispectral Measures and Feller markov Kernels
Semispectral Measure Markov Kernel C-algebras Quantum Mechanics
2012/7/11
It is well known \cite{B1,P} that a real positive semispectral measure $F$ is commutative if and only if there exist a self-adjoint operator $A$ and a Markov kernel $\mu_{(\cdot)}(\cdot):\sigma(A)\tim...
On projective modules for Frobenius kernels and finite Chevalley groups
projective modules Frobenius kernels finite Chevalley groups Group Theory
2012/4/23
Let $G$ be a simply-connected semisimple algebraic group scheme over an algebraically closed field of characteristic $p > 0$. Let $r \geq 1$ and set $q = p^r$. We show that if a rational $G$-module $M...
A remark on weighted bergman kernels on orbifolds
A remark weighted bergman kernels orbifolds
2018/4/19
In this note, we explain that Ross-Thomas’ result [4, Theorem 1.7] on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in...
Abstract: In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the co...
Markov property of determinantal processes with extended sine, Airy, and Bessel kernels
Determinantal processes Correlation kernels Random matrix theory Infinite particle systems Markov property Entire function and topology
2011/7/7
When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initi...
Kernels of Linear Representations of Lie Groups, Locally Compact Groups, and Pro-Lie Groups
Kernels of Linear Representations of Lie Groups Locally Compact Groups Pro-Lie Groups
2011/1/17
For a topological group G the intersection KOR(G) of all kernels of ordinary representations
is studied. We show that KOR(G) is contained in the center of G if G is a connected pro-Lie group.
Singular operators with antisymmetric kernels, related capacities, and Wolff potentials
Singular operators antisymmetric kernels related capacities Wolff potentials
2011/1/21
We consider a generalization of the Riesz operator in Rd and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version...
We study positive measures that are solutions to an abstract optimisation problem, which is a generalisation of a classical variational problem with a constraint on information of a Kullback-Leibler t...
Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation
manifold positive definite kernels least squares approximation Sobolev spaces
2011/2/24
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting.
We study positive measures that are solutions to an abstract optimisation problem, which is a generalisation of a classical variational problem with a constraint on information of a Kullback-Leibler t...