We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2. The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in a reproducing kernel Hilbert space (RKHS). Our results have implications to the analysi...

Abstract⎯We construct alternative frames of discernment from input belief functions. We assume that the core of each belief function is a subset of a so far unconstructed frame of discernment. The alternative frames are constructed as different cross products of unions of different cores. With the frames constructed the belief functions are combined for each alternative frame. The appropriatene...

In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a nite number of concentrated masses, elastic supports and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately deened Hilbert spa...

An Ad K invariant inner product on the Lie algebra of a compact connected Lie group K extends to a Hermitian inner product on the Lie algebra of the complexified Lie group Kc. The Laplace-Beltrami operator, ∆, on Kc induced by the Hermitian inner product determines, for each number a > 0, a Green’s function ra by means of the identity (a2−∆/4)−1 = ra∗. The Hilbert space of holomorphic functions...

In this paper we extend a methodology for constructing a frame of discernment from belief functions for one problem, into a methodology for constructing multiple frames of discernment for several different subproblems. The most appropriate frames of discernment are those that let our evidence interact in an interesting way without exhibit too much internal conflict. A function measuring overall...

This paper considers the problem of synthesizing the finite-word-length (FWL) two-dimensional (2-D) state-space filter structures with minimum weighted sensitivity. Two kinds of frequency-weighted sensitivity measures, one based on a mixture of L1=L2 norms and the other a pure L2 norm, are defined in place of the usual sensitivity measure and an upper bound expressed in terms of 2-D weighted Gr...

Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty lo, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz–Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a...

We introduce an integral-type operator, denoted by P φ , on the space of holomorphic functions on the unit ball B ⊂ C, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of P φ from the weighted Bergman space A p α B to the Bloch-type space Bμ B or the little Bloch-type space Bμ,0 B is calculated. The compactness of the operator is cha...

Let C be a field of subsets of a set I. It is well known that the space FA of all the finitely additive games of bounded variation on C is the norm dual of the space of all simple functions on C. In this paper we prove that the space BV of all the games of bounded variation on C is the norm dual of the space of all simple games on C. This result is equivalent to the compactness of the unit ball...

In this paper, the model reduction problem for state-space symmetric systems is investigated. First, it is shown that several model reduction methods, such as balanced truncation, balanced truncation which preserves the DC gain, optimal and suboptimal Hankel norm approximations, inherit the state-space symmetric property. Furthermore, for single input and single output (SISO) state-space symmet...