Given a strictly increasing continuous function φ from [0, 1] to [0, 1] and its pseudo-inverse φ [−1] , conditions that φ must satisfy for C φ (x 1, . . . ,x n)=φ [−1] (C(φ(x 1), . . . ,φ(x n))) to be a copula for any copula C are studied. Some basic properties of the copulas obtained in this way are analyzed and several examples of generator functions φ that can be used to construct copulas C φ are presented. In this manner, a method to obtain from a given copula C a variety of new copulas is provided. This method generalizes that used to construct Archimedean copulas in which the original copula C is the product copula, and it is related with mixtures Copyright Springer-Verlag 2005Probability distributions with given marginals, copulas, Archimedean copulas, mixtures,
The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogue to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We show that with this definition in many cases dual fusion frames behave similar to dual frames. We present examples of non-canonical dual fusion frames.Mathematics Subject Classification. Primary 42C15; Secondary 42C40, 46C99, 41A65.
A new notion of dual fusion frame has been recently introduced by the
authors. In this article that notion is further motivated and it is shown that
it is suitable to deal with questions posed in a finite-dimensional real or
complex Hilbert space, reinforcing the idea that this concept of duality solves
the question about an appropriate definition of dual fusion frames. It is shown
that for overcomplete fusion frames there always exist duals different from the
canonical one. Conditions that assure the uniqueness of duals are given. The
relation of dual fusion frame systems with dual frames and dual projective
reconstruction systems is established. Optimal dual fusion frames for the
reconstruction in case of erasures of subspaces, and optimal dual fusion frame
systems for the reconstruction in case of erasures of local frame vectors are
determined. Examples that illustrate the obtained results are exhibited
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