Related papers: Smoothness of Nonlinear and Non-Separable Subdivis…
In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix M=mI, m >=2, and present a general approach for checking their convergence and for determining their H\"older regularity. The…
A systematic and comprehensive study of p-adic refinement equations and subdivision scheme associated with a finitely supported refinement mask are carried out in this paper. The Lq -convergence of the subdivision scheme is characterized in…
This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a…
We present a framework for analyzing non-linear $\mathbb{R}^d$-valued subdivision schemes which are geometric in the sense that they commute with similarities in $\mathbb{R}^d$. It admits to establish $C^{1,\alpha}$-regularity for arbitrary…
This paper extends the matrix based approach to the setting of multiple subdivision schemes studied in [Sauer 2012]. Multiple subdivision schemes, in contrast to stationary and non-stationary schemes, allow for level dependent subdivision…
This paper studies well-defindness and convergence of subdivision schemes which operate on Riemannian manifolds with nonpositive sectional curvature. These schemes are constructed from linear ones by replacing affine averages by the…
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…
In this paper we define a family of nonlinear, stationary, interpolatory subdivision schemes with the capability of reproducing conic shapes including polynomials upto second order. Linear, non-stationary, subdivision schemes do also…
We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…
Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…
This paper presents a detailed regularity analysis of anisotropic wavelet frames and subdivision. In the univariate setting, the smoothness of wavelet frames and subdivision is well understood by means of the matrix approach. In the…
In this paper, we present a new matrix approach for the analysis of subdivision schemes whose non-stationarity is due to linear dependency on parameters whose values vary in a compact set. Indeed, we show how to check the convergence in…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
In this paper we investigate $L^p$ and Sobolev boundedness of a certain class of pseudodifferential operators with non-regular symbols. We employ regularisation methods, namely convolution with a net of mollifiers $(\rho_\eps)_\eps$, and we…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…
In this paper we are concerned with $L^p$-maximal parabolic regularity for abstract nonautonomous parabolic systems and their quasilinear counterpart in negative Sobolev spaces incorporating mixed boundary conditions. Our results are…
Smooth pseudodifferential operators on $\mathbb{R}^n$ can be characterized by their mapping properties between $L^p-$Sobolev spaces due to Beals and Ueberberg. In applications such a characterization would also be useful in the non-smooth…