We introduce the concept of weak Lyapunov similarity on linear systems. And we obtain that bounded linear systems with pure point spectrum is weak Lyapunov similar to constant coefficient diagonal linear systems.
Let G be a second countable locally compact Groupoid with Haar measure, H be a closed subgropoid of G, then we can get a Groupoid H\G2. We have proved C*(H) is Morita equivalent to C*(H\G2), which is a problem in [1]. Using the imprimitive bimodule and a homomorphism from C*(G) to M(G*(H\G2)) the induced representation from C*(H) to C*(G) is obtained.Particularly in the case of group bundles, we define a homomorphism from C*(H) to M(C*(G)) and obtain the integral form of the induced representation.
In this paper, we establish generalized inverses of functors. We obtain that: (1) generalized inverses of functors include generalized inverses of matrices by not looking matrices as morphisms,(2) generalized inverses of functors are different from generalized inverses of morphisms, but they have the same applications in many ways.
In this paper we gave some equivalent conditions of the fractional derivative and integral of holomorphic function f on Ω to belong to the mixed norm spaces H(p,q,)on bounded symmetric domains Ω of Cn, where 0 < p, q < and is a normal function. Applying these results, for two cases 0
