ABSTRACT
This chapter shows that in the result of R. Meise and D. Vogt we can remove the condition that locally convex space is of Hilbert type, that is to say, we prove that every entire function / of uniformly bounded type on the nuclear locally convex space over C can be extended holomorphically to the Hilbert type locally convex space. The proof of the main result is based on the tensor product representation of η-homogeneous polynomials. The chapter outlines some notation, definitions and basic properties of locally convex spaces. It shows that every entire function of uniformly bounded type on the nuclear locally convex space can be extended holomorphically to the locally convex space so that nuclear convex space is a topological linear subspace of convex space.
