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This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

In this paper the problem of system equivalence is tackled for a rather general class of linear time-invariant systems. We consider AR-systems described by linear continuous shift-invariant operators with finite memory, acting on Frechet-signal spaces, containing the space £(lR) of infinitely differentiable functions on lR. This class is in one-one correspondence with matrices of suitable sizes...

The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, t-function: definition for Numer. Linear Algebra Appl. 27 (3), e2288]. In this work, we investigate properties Fr\'echet derivative t-function and derive algorithms its efficient numerical computation. Applications condition number estimation nuclear ...

1. ip is real-analytic; 2. the rank of <p equals p on an everywhere dense subset of U; 3. (f(U) is closed in V; 4. for each compact subset K C <p(U), there exists a compact subset H C U such that <p(H) = K. Then the composition subalgebra A? = {foip: f e C°°(V)} is closed in C°°(U), when this algebra carries its natural Frechet topology (convergence on compact subsets of the function and all it...

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...