Extension by integer translates of compactly supported function for multiplier spaces on periodic Hardy spaces to multiplier spaces on Hardy spaces is given . Shannon sampling theorem is extende d to Hardy spaces. 1 . Introduction and statement of results The purpose of this paper is to establish a natural extension from multiplier spaces M(p) on periodic Hardy spaces HP (T) to multiplie r spac...

In this paper, we study three types of rotational surfaces in Galilean 3-spaces. We classify satisfying $$L_1G=F(G+C)$$ for some constant vector $C\in \mathbb{G}^3$ and smooth function $F$, where $L_1$ denotes the Cheng-Yau operator.

Let ǫ > 0. A continuous linear operator T : C(X) −→ C(Y ) is said to be ǫ-disjointness preserving if ‖(Tf)(Tg)‖ ∞ ≤ ǫ, whenever f, g ∈ C(X) satisfy ‖f‖ ∞ = ‖g‖ ∞ = 1 and fg ≡ 0. In this paper we address basically two main questions: 1.How close there must be a weighted composition operator to a given ǫ-disjointness preserving operator? 2.How far can the set of weighted composition operators be ...

The column space of a real n× k matrix x of rank k is a k-plane. Thus we get a map from the space X of such matrices to the Grassmannian G of k-planes in Rn, and hence a GLn-equivariant isomorphism C∞ (G) ≈ C∞ (X)k . We consider the On ×GLk-invariant differential operator C on X given by C = det ( xx ) det ( ∂∂ ) , where x = (xij) , ∂ = ( ∂ ∂xij ) . By the above isomorphism C defines an On-inva...

Stampfli has shown that for a given T £ B(H) there exists a K £ C(H) so that o(T + K) = ow(T). An analogous result holds for the essential numerical range We(T). A compact operator K is said to preserve the Weyl spectrum and essential numerical range of an operator T £ B(H) if o(T + K) = o„(T) and W(T + K)= We(T). Theorem. For each block diagonal operator T, there exists a compact operator K wh...