The Experts below are selected from a list of 210 Experts worldwide ranked by ideXlab platform
Zhenqing Chen - One of the best experts on this subject based on the ideXlab platform.
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heat kernel estimates and parabolic harnack inequalities for Symmetric dirichlet Forms
Advances in Mathematics, 2020Co-Authors: Zhenqing Chen, Takashi Kumagai, Jian WangAbstract:Abstract In this paper, we consider the following Symmetric Dirichlet Forms on a metric measure space ( M , d , μ ) : E ( f , g ) = E ( c ) ( f , g ) + ∫ M × M ( f ( x ) − f ( y ) ) ( g ( x ) − g ( y ) ) J ( d x , d y ) , where E ( c ) is a strongly local Symmetric Bilinear Form and J ( d x , d y ) is a Symmetric Radon measure on M × M . Under general volume doubling condition on ( M , d , μ ) and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp. two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp. the Poincare inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to Symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2.
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heat kernel estimates and parabolic harnack inequalities for Symmetric dirichlet Forms
arXiv: Probability, 2019Co-Authors: Zhenqing Chen, Takashi Kumagai, Jian WangAbstract:In this paper, we consider the following Symmetric Dirichlet Forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a strongly local Symmetric Bilinear Form and $J(dx,dy)$ is a Symmetric Random measure on $M\times M$. Under general volume doubling condition on $(M,d,\mu)$ and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp.\ two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp.\ the Poincar\'e inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to Symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than $2$.
Jian Wang - One of the best experts on this subject based on the ideXlab platform.
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heat kernel estimates and parabolic harnack inequalities for Symmetric dirichlet Forms
Advances in Mathematics, 2020Co-Authors: Zhenqing Chen, Takashi Kumagai, Jian WangAbstract:Abstract In this paper, we consider the following Symmetric Dirichlet Forms on a metric measure space ( M , d , μ ) : E ( f , g ) = E ( c ) ( f , g ) + ∫ M × M ( f ( x ) − f ( y ) ) ( g ( x ) − g ( y ) ) J ( d x , d y ) , where E ( c ) is a strongly local Symmetric Bilinear Form and J ( d x , d y ) is a Symmetric Radon measure on M × M . Under general volume doubling condition on ( M , d , μ ) and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp. two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp. the Poincare inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to Symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2.
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heat kernel estimates and parabolic harnack inequalities for Symmetric dirichlet Forms
arXiv: Probability, 2019Co-Authors: Zhenqing Chen, Takashi Kumagai, Jian WangAbstract:In this paper, we consider the following Symmetric Dirichlet Forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a strongly local Symmetric Bilinear Form and $J(dx,dy)$ is a Symmetric Random measure on $M\times M$. Under general volume doubling condition on $(M,d,\mu)$ and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp.\ two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp.\ the Poincar\'e inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to Symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than $2$.
Mozhei N. P. - One of the best experts on this subject based on the ideXlab platform.
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Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces. II
2020Co-Authors: Mozhei N. P.Abstract:We describe all invariant affine connections on three-dimensional pseudo-Riemannian homogeneous spaces. We present the complete local classification of pseudo-Riemannian homogeneous spaces. It is equivalent to the description of effective pairs of Lie algebras supplied with an invariant nondegenerate Symmetric Bilinear Form on the isotropy module
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Affine connections on three-dimensional pseudo-Riemannian homogeneous spaces.
2020Co-Authors: Mozhei N. P.Abstract:The aim of this paper is to describe all invariant affine connections on pseudo-Riemannian homogeneous spaces of dimensions 2 and 3. We present a complete local classification of Riemannian homogeneous spaces which is equivalent to the description of effective pairs of Lie algebras supplied with an invariant nondegenerate Symmetric Bilinear Form on the isotropy module
Mohammed Guediri - One of the best experts on this subject based on the ideXlab platform.
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corrigendum to novikov algebras carrying an invariant lorentzian Symmetric Bilinear Form j geom phys 82 2014 132 144
Journal of Geometry and Physics, 2016Co-Authors: Mohammed GuediriAbstract:Abstract The purpose of this note is to correct the classification list of Novikov algebras admitting an invariant Lorentzian Symmetric Bilinear Form in our paper mentioned above.
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novikov algebras carrying an invariant lorentzian Symmetric Bilinear Form
Journal of Geometry and Physics, 2014Co-Authors: Mohammed GuediriAbstract:Abstract In this note, we shall classify Novikov algebras that admit an invariant Lorentzian Symmetric Bilinear Form.
Takashi Kumagai - One of the best experts on this subject based on the ideXlab platform.
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heat kernel estimates and parabolic harnack inequalities for Symmetric dirichlet Forms
Advances in Mathematics, 2020Co-Authors: Zhenqing Chen, Takashi Kumagai, Jian WangAbstract:Abstract In this paper, we consider the following Symmetric Dirichlet Forms on a metric measure space ( M , d , μ ) : E ( f , g ) = E ( c ) ( f , g ) + ∫ M × M ( f ( x ) − f ( y ) ) ( g ( x ) − g ( y ) ) J ( d x , d y ) , where E ( c ) is a strongly local Symmetric Bilinear Form and J ( d x , d y ) is a Symmetric Radon measure on M × M . Under general volume doubling condition on ( M , d , μ ) and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp. two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp. the Poincare inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to Symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2.
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heat kernel estimates and parabolic harnack inequalities for Symmetric dirichlet Forms
arXiv: Probability, 2019Co-Authors: Zhenqing Chen, Takashi Kumagai, Jian WangAbstract:In this paper, we consider the following Symmetric Dirichlet Forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a strongly local Symmetric Bilinear Form and $J(dx,dy)$ is a Symmetric Random measure on $M\times M$. Under general volume doubling condition on $(M,d,\mu)$ and some mild assumptions on scaling functions, we establish stability results for upper bounds of heat kernel (resp.\ two-sided heat kernel estimates) in terms of the jumping kernels, the cut-off Sobolev inequalities, and the Faber-Krahn inequalities (resp.\ the Poincar\'e inequalities). We also obtain characterizations of parabolic Harnack inequalities. Our results apply to Symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than $2$.
