In this paper we presented an extension of previous results given in the papers [15], [17],[19], main idea proofs is: write down difference trigonometric kernel general expansion considered, and have to estimate resulting infinite sums. For terms these sums used sharper different estimates than literature (the most exact where by V.A.Il’n, I. Joó V.Komornik).

A method for simultaneously approximating to high accuracy the corresponding eigenvalue and zeros of the (n + l)st eigenfunction of a regular Sturm-Liouville eigenvalue problem is presented. It is based upon equilibrating the minimum eigenvalues of several problems on subintervals that form a partition of the orginal interval. The method is easily derived from classical mini-max variational pri...

When partitioning the variation of univariate or multivariate ecological data with respect to several submodels of spatial eigenfunctions (e.g., Moran's eigenvector maps, MEM) acting as explanatory data, a problem occurs: although the submodels are constructed to be orthogonal to one another, the partitioning based on adjusted R2 statistics produces nonzero values in the intersections between s...

In recent years several high quality Sturm-Liouville software packages have been written (e.g., SLEDGE, SLEIGN, the NAG routine SL02FM). All excel at providing eigenfunction estimates at a nite set of points but only the NAG routine provides interpolation capability, and this by a fairly crude method (especially when compared with the sophistication of its eigenvalue solver). We describe an acc...