Radial basis functions and corresponding zonal series expansions on the sphere
نویسندگان
چکیده
Since radial positive definite functions on R remain positive definite when restricted to the sphere, it is natural to ask for properties of the zonal series expansion of such functions which relate to properties of the Fourier-Bessel transform of the radial function. We show that the decay of the Gegenbauer coefficients is determined by the behavior of the Fourier-Bessel transform at the origin. 2000 AMS subj. class.: 42C10, 42A82, 33C10, 33C45
منابع مشابه
Stable Gaussian radial basis function method for solving Helmholtz equations
Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems. They are often referred to as a meshfree method and can be spectrally accurate. In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion. We develop our approach in two-dimensional spaces for so...
متن کاملAnalysis on Centrifugal Load Effect in FG Hollow Sphere Subjected to Magnetic Field
This paper presents the effect of centrifugal load in functionally graded (FG) hollow sphere subjected to uniform magnetic field. Analytical solution for stresses and perturbation of the magnetic field vector are determined using the direct method and the power series method. The material stiffness, the magnetic permeability and the density vary continuously across the thickness direction accor...
متن کاملA meshless method for optimal control problem of Volterra-Fredholm integral equations using multiquadratic radial basis functions
In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...
متن کاملInterpolation with reflection invariant positive definite functions
Concepts of abstract harmonic analysis can be used to provide a unifying framework for basis function methods, like radial basis functions in Euclidean spaces or zonal basis functions on the sphere. To illustrate how these concepts can be applied reflection invariant functions are considered. A specialization of the BochnerGodement Theorem leads to a characterization of suitable basis functions. §
متن کاملNative Hilbert Spaces for Radial Basis Functions II
This contribution continues an earlier survey 20] over the native spaces associated to (not necessarily radial) basis functions. After recalling the basics, the relation to L 2 spaces is studied. This leads to a new formulation of the theory of radial basis functions in the context of integral operators. Instead of Fourier transforms, the most important tools now are expansions into eigenfuncti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 134 شماره
صفحات -
تاریخ انتشار 2005