Decompositions of Gelfand–Shilov kernels into kernels of similar class

Smooth Wavelet Decompositions with Blocky Coecient Kernels

We describe bases of smooth wavelets where the coe cients are obtained by integration against ( nite combinations of) boxcar kernels rather than against traditional smooth wavelets. Bases of this type were rst developed in work of Tchamitchian and of Cohen, Daubechies, and Feauveau. Our approach emphasizes the idea of average-interpolation { synthesizing a smooth function on the line having pre...

Efficient anisotropic α-Kernels decompositions and flows

The Laplacian raised to fractional powers can be used to generate scale spaces as was shown in recent literature. This was later extended for inhomogeneous diffusion processes and more general functions of the Laplacian and studied for the Perona-Malik case. In this paper we extend the results to the truly anisotropic Beltrami flow. We additionally introduce a technique for splitting up the wor...

Smooth Wavelet Decompositions with Blocky Coeecient Kernels

We describe bases of smooth wavelets where the coeecients are obtained by integration against ((nite combinations of) boxcar kernels rather than against traditional smooth wavelets. Bases of this type were rst developed in work of Tchamitchian and of Cohen, Daubechies, and Feauveau. Our approach emphasizes the idea of average-interpolation { synthesizing a smooth function on the line having pre...

A New Class of Spatial Covariance Functions Generated by Higher-order Kernels

Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier transform of some higher-order kernels. Moreover, we extend this class of spatial covariance functions to the spatio-temporal setting using the idea used in...

Reproducing kernels , Bergman kernels , Poisson kernels