The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials,...There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.展开更多
A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions....A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.展开更多
In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.
Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. ...Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has展开更多
基金NSF Grant #DMS-89-01345ARO Contract DAAL 03-90-G-0091
文摘The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
文摘There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.
文摘A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.
文摘In this note, we establish a companion result to the theorem of J. Szabados on the maximum of fundamental functions of Lagrange interpolation based on Chebyshev nodes.
文摘Let D={z∈C: │z│【1} be the unit disk in the finite complex plane C and Г a Fuchsiangroup consisting of Mbius maps from D to itself. Also, let Ω={z∈D:│z│【│γz│, id≠γ∈Г}be the fundamental region unde Г. Put Ω=D when Г={id}. If we denote by Ω andΩ the closure and boundary of Ω on D, respectively, then we know that Ω has
