Function spaces on singular manifolds

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Examples of singular normal complex spaces which are topological manifolds.

In case V is irreducible with singular curve C, we cannot write every oeH3(W V) as a tube. Indeed, oa = 6C4 and C4 Will meet C in a finite number of points. The trouble is similar to the above and may be overcome as follows: Let DC V be a curve meeting C transversely at a finite number of points pi,...pt. For simplicity, assume t = 1, p = pi, and let B be a small ball around p in W. We may assu...

Compact and strictly singular operators on certain function spaces

On G-function of Frobenius manifolds related to Hurwitz spaces

Abstract. The semisimple Frobenius manifolds related to the Hurwitz spaces Hg,N(k1, . . . , kl) are considered. We show that the corresponding isomonodromic tau-function τI coincides with (−1/2)power of the Bergmann tau-function which was introduced in a recent work by the authors [8]. This enables us to calculate explicitly the G-function of Frobenius manifolds related to the Hurwitz spaces H0...

Graph Laplacians on Singular Manifolds: Toward understanding complex spaces: graph Laplacians on manifolds with singularities and boundaries

In manifold learning, algorithms based on graph Laplacian constructed from data have received considerable attention both in practical applications and theoretical analysis. Much of the existing work has been done under the assumption that the data is sampled from a manifold without boundaries and singularities or that the functions of interest are evaluated away from such points. At the same t...