The Matérn family of covariance functions has played a central role in spatial statistics for decades, being flexible parametric class with one parameter determining the smoothness paths underlying field. This paper proposes functions, which stems from reparameterization generalized Wendland family. As case, proposed allows continuous parameterization Gaussian random field, additionally compact...

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in number ways, including as colimit homeomorphism groups with given compact support, or subgroup the its Stone-\v{C}ech compactification. A is said to have Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. authors provide necessary and sufficient conditions for finite produ...

Although tensor product real-valued wavelets have been successfully applied to many high-dimensional problems, they can only capture well edge singularities along the coordinate axis directions. As an alternative and improvement of tensor product real-valued wavelets and dual tree complex wavelet transform, recently tensor product complex tight framelets with increasing directionality have been...

We find existence of a nonnegative compactly supported solution of the problem ∆u = uα in R+ , ∂u ∂ν = u on ∂R+ . Moreover, we prove that every nonnegative solution with finite energy is compactly supported and radially symmetric in the tangential variables.

We study tight wavelet frames associated with symmetric compactly supported re-nable functions, which are obtained with the unitary extension principle. We give a criterion for existence of two symmetric or antisymmetric compactly supported framelets. All reenable masks of length up to 6, satisfying this criterion, are found.

Chui and Wang discussed the construction of one-dimensional compactly supported wavelets under a general framework, and constructed one-dimensional compactly supported spline wavelets. In this paper, under a mild condition, the construction of M = ( 1 1 1 −1 )-wavelets is obtained.

We consider Lebesgue{integrable, compactly supported solutions of two{ scale diierence equations and investigate the relations between translates of these solutions. A detailed study of corresponding invariant subspaces leads to new observations concerning the factorization of the reenement mask and certain spectral properties of corresponding coeecient matrices. In particular, new necessary co...

‎The sequences of the form ${E_{mb}g_{n}}_{m‎, ‎ninmathbb{Z}}$,‎ ‎where $E_{mb}$ is the modulation operator‎, ‎$b>0$ and $g_{n}$ is the‎ ‎window function in $L^{2}(mathbb{R})$‎, ‎construct Fourier-like‎ ‎systems‎. ‎We try to consider some sufficient conditions on the window‎ ‎functions of Fourier-like systems‎, ‎to make a frame and find a dual‎ ‎frame with the same structure‎. ‎We also extend t...