Eigenvalue sequences of positive integral operators and moduli of smoothness
We utilize moduli of smoothness and K-functionals as new tools in the arena of estimating the decay rates of eigenvalue sequences associated with some commonly used positive integral operators on spheres. This approach is novel and effective. We develop two readily verifiable and implementable conditions for the kernels of the integral operators under which favorable decay rates of eigenvalue sequences are derived. The first one (based on spherical mean operators) is an enhancement of the classical Hölder condition. The second one, works seamlessly with the Laplace-Beltrami operators and can be applied directly to Bessel potential kernels.
Decay rates, Fourier coefficients, Moduli of smoothness, Positive integral operators, Sphere
Jordão, T., V. A. Menegatto, and Xingping Sun. "Eigenvalue sequences of positive integral operators and moduli of smoothness." In Approximation theory XIV: San Antonio 2013, pp. 239-254. Springer, Cham, 2014.
Springer Proceedings in Mathematics and Statistics