We consider the relationship between derivations and local power series quotients for a locally multiplicatively convex Fr echet algebra (this includes the case of a Banach algebra). In x2 we derive necessary conditions for a commutative Fr echet algebra to have a local power series quotient. Our main result here is Proposition 2.6, which shows that if the generating element has nite closed des...

For some heuristic approaches of the boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity eld or material derivative method are discussed. Moreover, for some of these approaches the funcionals are Fr echet-diierentiable, because an embedding into a Banach space problem is possi...

We give an integrability criterion for a projective limit of Banach distributions on Fr\'echet manifold which is manifolds. This leads to result involutive bundles sequence can be seen as version Frobenius Theorem in setting. As consequence, we obtain the third Lie theorem Fr\'echet-Lie group submersive groups. also application prolongations algebroid.

1991 Abstract. A topological space X is called A-real compact, if every algebra homomorphism from A to the reals is an evaluation at some point of X, where A is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In AdR] it was shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex ...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr echet distance. Whereas e cient algorithms are known for computing the Fr echet distance of polygonal curves, the same problem for triangulated surfaces is NP-hard. Furthermore, it remained open whether it is computable at all. Using a discrete approximation we show that it is upper semi-co...

For Fr$acute{mathbf{text{e}}}$chet algebras $(A, (p_n))$ and $(B, (q_n))$, a linear map $T:Arightarrow B$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(Tab - Ta Tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{N}$, $a, b in A$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$...