A series representation of the discrete fractional Laplace operator of arbitrary order

نویسندگان

چکیده

Although fractional powers of non-negative operators have received much attention in recent years, there is still little known about their behavior if real-valued exponents are greater than one. In this article, we define and study the discrete Laplace operator arbitrary positive order. A series representation for non-integer developed. Its convergence to a case integer proven as power tends value. Furthermore, show that new consistent with existing theoretical results.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Adaptive Discrete Laplace Operator

Diffusion processes capture information about the geometry of an object such as its curvature, symmetries and particular points. The evolution of the diffusion is governed by the Laplace-Beltrami operator which presides to the diffusion on the manifold. In this paper, we define a new discrete adaptive Laplacian for digital objects, generalizing the operator defined on meshes. We study its eigen...

متن کامل

A Laplace Operator on Semi-Discrete Surfaces

This paper studies a Laplace operator on semi-discrete surfaces. A semidiscrete surface is represented by a mapping into three-dimensional Euclidean space possessing one discrete and one continuous variable. It can be seen as a limit case of a quadrilateral mesh, or as a semi-discretization of a smooth surface. Laplace operators on both smooth and discrete surfaces have been an object of intere...

متن کامل

Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes

We derive a nonlinear stabilized Galerkin approximation of the Laplace operator for which we prove a discrete maximum principle on arbitrary meshes and for arbitrary space dimension without resorting to the well-known acute condition or generalizations thereof. We also prove the existence of a discrete solution and discuss the extension of the scheme to convection-diffusion-reaction equations. ...

متن کامل

Eigenvalues of the fractional Laplace operator in the unit ball

We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (−∆)α/2 in the unit ball D ⊂ Rd, with a Dirichlet condition in the complement of D. The standard Rayleigh–Ritz variational method is used for the upper bounds, while the lower bounds involve the less-known Aronszajn method of intermediate problems. Both require exp...

متن کامل

ذخیره 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 Analysis and Applications

سال: 2021

ISSN: ['0022-247X', '1096-0813']

DOI: https://doi.org/10.1016/j.jmaa.2021.125323