The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov–type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...

The Catmull-Clark subdivision algorithm consists of an operator that can be decomposed into a refinement operator and a successively executed smoothing operator, where the refinement operator splits each face with m vertices into m quadrilateral subfaces and the smoothing operator replaces each internal vertex with an affine combination of its neighboring vertices and itself. Over regular meshe...

We introduce a modified version of the Whitney extension operators for collections functions from closed subset Rn into scales Banach spaces with smoothing operators. prove an theorem whose elements take values in different scale. A motivation considering this kind comes very basic observations on composition more than one real variable. The idea at base proof is rather natural context spaces, ...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

Figure 1. Convergence factors for various discretizations of the Laplacian (Case 1). The lines show smoothing factors of optimally weighted point Jacobi (solid line), line Jacobi (dashes), and unweighted point RB (alternating dashes). The symbols correspond to numerical calculations using V(1,0) cycles with point Jacobi (), line Jacobi (+), and point RB (2), and also two-level (1,0) cycles usin...

This paper proposes a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed Finite-Element/Finite-Volume method, and compare them to existing formulations...

A piecewise linear (PWL) function approximation scheme is described by a lattice algebra of modified operators that allows for the interpolation of PWL function vertexes. A new recursive method called Centred Recursive Interpolation (CRI) based on such modified operators is analysed for successive function smoothing and more accurate approximation. This approximation method, simple but accurate...