Compared to scalar framelets, multiframelets have certain advantages, such as relatively smaller supports on generators, high vanishing moments, etc. The balancing property of is very desired, it reflects how efficient vector-valued data can be processed under the corresponding discrete multiframelet transform. Most literature studying balanced from point view function setting, but few approach...

Abstract We describe some sufficient conditions, under which smooth and compactly supported functions are or not dense in the fractional Sobolev space $$W^{s,p}(\Omega )$$ W s , p ( Ω <mml:mo...

Using results on syzygy modules over a multivariate polynomial ring, we are able to construct compactly supported wavelet bi-frames with few generators from almost any pair of compactly supported multivariate refinable functions. In our examples, we focus on wavelet bi-frames whose primal and dual wavelets are both derived from one box spline function. Our wavelet bi-frames have fewer generator...

In this paper, we consider Barenblatt’s k– model for turbulence. For the case of equal diffusion coefficients α and β, Barenblatt found explicit compactly supported self-similar solutions. From these, we obtain compactly supported solutions for α 6= β by transforming the equations into a four-dimensional quadratic system and verifying a transversality condition for a saddle-point connection. Th...

We analyze the spectral shift function (SSF) of a Schrödinger operator due to a compactly supported potential. We give a bound on the integral of the SSF with respect to a bounded compactly supported function. It is based on the control of the singular values of the difference of two Schrödinger semigroups. As an application we improve some earlier results on the regularity of the integrated de...

The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an accepted method for machine learning, one of the foundations of mesh-free methods, an alternative way to construct higher order methods for solving partial differential equations (PDEs), an emerging method for solving PDEs on surfaces, ...

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function φ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function φ is compactly supported conjugate symmetric, then we prove that there exists a compactly s...

Compactly supported wavelet bases for Sobolev spaces is investigated. Steming from a pair of compactly supported refinale functions with multiscale dilation factor in space 2 3 ( ) L R meeting a very mild condition, we provide a general approach for constructing wavelet bases, which is the generalization of univariate wavelets in Hilbert space. The notion of orthogonal non-tensor product trivar...

Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinati...