On images of continuous functions from a compact manifold to Euclidean space

on images of continuous functions from a compact manifold to euclidean space

Spherical Functions on Euclidean Space

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space En = G/K where G is the semidirect product Rn · K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space of (G,K)–spherical functions by a certain affine algebraic variety, and of the positive definite on...

Continuous Functions on Compact Groups

We show that every scalar valued continuous function f(g) on a compact group G may be written as f(g) = 〈Φ(g)ξ, η〉 for all g ∈ G, where ξ, η are vectors in a separable Hilbert space H, and Φ(g) is a strongly continuous unitary valued function on G which is a product of unitary representations and antirepresentations of G on H. This product is countable, but always converges uniformly on G. More...

compact hypersurfaces in euclidean space and some inequalities

let (m,g ) be a compact immersed hypersurface of (rn+1,) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, a the shape operator, vol (m ) the volume of m,and s the scalar curvature of m. in this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2m ma dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2m 1 mdv s dvn nα ρ ≥ ρ∫ − ∫ ,3) if the scalar curvatu...

from linguistics to literature: a linguistic approach to the study of linguistic deviations in the turkish divan of shahriar

chapter i provides an overview of structural linguistics and touches upon the saussurean dichotomies with the final goal of exploring their relevance to the stylistic studies of literature. to provide evidence for the singificance of the study, chapter ii deals with the controversial issue of linguistics and literature, and presents opposing views which, at the same time, have been central to t...

From vortices to instantons on the Euclidean Schwarzschild manifold

The first irreducible solution of the SU(2) self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on R were discovered. While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on R, the case of the Euclidean Schwarzschild manifold has res...