Heat kernel expansion for operators containing a root of the Laplace operator
نویسندگان
چکیده
منابع مشابه
Heat Kernel Expansion for Operators of the Type of the Square Root of the Laplace Operator
A method is suggested for the calculation of the DeWitt-Seeley-Gilkey (DWSG) coefficients for the operator √ −∇2 + V (x) basing on a generalization of the pseudodifferential operator technique. The lowest DWSG coefficients for the operator √ −∇2 + V (x) are calculated by using the method proposed. It is shown that the method admits a generalization to the case of operators of the type (−∇2 + V ...
متن کاملHeat Kernel Laplace-Beltrami Operator on Digital Surfaces
Many problems in image analysis, digital processing and shape optimization can be expressed as variational problems involving the discretization of the Laplace-Beltrami operator. Such discretizations have have been widely studied for meshes or polyhedral surfaces. On digital surfaces, direct applications of classical operators are usually not satisfactory (lack of multigrid convergence, lack of...
متن کاملHeat-kernel coefficients of the Laplace operator on the D-dimensional ball
We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and integrals and skilful analytic continuation of zeta functions on the complex plane. We apply our method to the case of the heat-kernel expansion of the Laplace o...
متن کاملHeat-kernel coefficients of the Laplace operator on the 3-dimensional ball
We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle) arbitrary number of heat-kernel coefficients for the case where the basis functions are known. New results for the coefficients B 5 2 , ..., B5 are presented. ∗Al...
متن کاملA remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator
We adapt in the present note the perturbation method introduced in [3] to get a lower Gaussian bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1997
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.531823