• Publications
  • Influence
Characterization of scaling functions in a multiresolution analysis
We characterize the scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear map A: R n → R n suchExpand
  • 31
  • 5
  • PDF
Characterization of low pass filters in a multiresolution analysis
We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by aExpand
  • 14
  • 1
  • PDF
A family of nonseparable scaling functions and compactly supported tight framelets
Abstract Given integers b and d , with d > 1 and | b | > 1 , we construct even nonseparable compactly supported refinable functions with dilation factor b that generate multiresolution analyses on LExpand
  • 6
  • PDF
Compactly supported Parseval framelets with symmetry associated to matrices
TLDR
We construct two families of Parseval wavelet frames with two generators. Expand
  • 3
Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space
Abstract We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T ( u ) = − ∫ R d K ( x , y ) ( u ( y ) − u ( x ) ) d y . Here we consider a kernel K ( xExpand
  • 10
  • PDF
Equivalence of A-Approximate Continuity for Self-Adjoint Expansive Linear Maps
Let A be an expansive linear map from R^d to R^d. The notion of A-approximate continuity was recently used to give a characterization of scaling functions in a multiresolution analysis (MRA). TheExpand
  • 4
  • PDF
Decay estimates for nonlinear nonlocal diffusion problems in the whole space
AbstractIn this paper, we obtain bounds for the decay rate in the Lr (ℝd)-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, $$u_t \left( {x,t} \right) =Expand
  • 7
  • PDF
On translation invariant multiresolution analysis
We give a characterization of the scaling functions and low pass filters in a translation invariant multiresolution analysis on L2(R). Our conditions involve the notion of locally non-zero function.Expand
  • 1
  • PDF
On the orthogonal democratic systems in the $L^p$ spaces
The concept of bidemocratic pair for a Banach space was introduced in \cite{KS:18}. We construct a family of orthonormal systems $\mathfrak{F}_{l},$ $l\in (0,\infty)$ of functions defined on $[-1,1]$Expand