Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential

Stepin S.A.

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Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential

机译：半群核的渐近估计，该估计是由双调和算子的电势扰动产生的

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Asymptotic formulae and estimates for the integral kernel of the semigroup generated by a perturbation of the bi-Laplacian by a potential are established by the parametrix method. These formulae are found using an approach which is conceptually close to the probabilistic approach used to calculate the coefficients of a short-time expansion for the heat kernel and based on the representation of this kernel as a Wiener integral. As an application, an asymptotic formula for the regularized trace of the operator semigroup under consideration is found. Bibliography: 19 titles.

机译：通过parametrix方法建立了通过势对双Laplacian进行扰动而生成的半群积分核的渐近公式和估计。这些公式是使用一种概念上接近于概率方法的方法找到的，该方法用于计算热核的短时膨胀系数，并且基于该核作为维纳积分的表示。作为一个应用，找到了考虑中的算子半群的正则迹线的渐近公式。参考书目：19种。

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《Sbornik. Mathematics》 |2012年第6期|共29页
作者
Stepin S.A.;
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正文语种 eng
中图分类数学;
关键词
Born approximation; Operator semigroup; Parametrix expansion; Regularized trace; Short-time asymptotics;

机译：Born逼近;算子半群;Parametrix展开;正则迹线;短期渐近性;

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专利

1. Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential [J] . Stepin S.A. Sbornik. Mathematics . 2012,第5a6期

机译：半群核的渐近估计，该估计是由双调和算子的电势扰动产生的
2. Existence and Global Asymptotical Stability of Periodic Solution for the 7 -Periodic Logistic System with Time-Varying Generating Operators and To-Periodic Impulsive Perturbations on Banach Spaces [J] . JinRong Wang, X. Xiang, W. Wei, Discrete dynamics in nature and society . 2008,第1期

机译：具有时变生成算子和Banach空间上的周期脉冲摄动的7周期Logistic系统周期解的存在性和全局渐近稳定性
3. Existence and Global Asymptotical Stability of Periodic Solution for theT-Periodic logistic System with Time-Varying Generating Operators andT0-Periodic Impulsive Perturbations on Banach Spaces [J] . JinRongWang, X.Xiang, W.Wei, Discrete dynamics in nature and society . 2008,第5期

机译：具有时变生成算子和T0-周期脉冲扰动的T-周期物流系统周期解的存在性和全局渐近稳定性
4. THE LAYER POTENTIALS OF SOME PARTIALDIFFERENTIAL OPERATORS: REAL ANALYTICDEPENDENCE UPON PERTURBATIONS [C] . M. DALLA RIVA International Society for Analysis, Applications, and Computation . 2009

机译：一些部分特化运营商的层势：扰动时真实的分析依赖性
5. The Szego Kernel of Certain Polynomial Models, and Heat kernel Estimates for Schroedinger Operators with Reverse Hoelder Potentials. [D] . Tinker, Michael. 2014

机译：某些多项式模型的Szego核以及具有反向Hoelder势的Schroedinger算子的热核估计。
6. Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator [O] . Der-Chen Chang, Yutian Li -1

机译：Heisenberg次拉普拉斯算子和Grushin算子的热核渐近展开
7. Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic Logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces [O] . JinRong Wang, X. Xiang, W. Wei, 2008

机译：Banach空间上具有时变生成算子和T0-周期脉冲扰动的T-周期Logistic系统周期解的存在性和全局渐近稳定性
8. Nonlinear Perturbations of Differential Operators with Nontrivial Kernel and Applications to Third Order Periodic Boundary Value Problems. [R] . Afuwape, A. U., Omari, P., Zanolin, F. 1987

机译：非平凡核微分算子的非线性扰动及其在三阶周期边值问题中的应用。

Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential

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