A Hilbert space approach to self-similar systems
نویسنده
چکیده
This paper investigates the structural properties of linear self-similar systems, using an invariant subspace approach. The self-similar property is interpreted in terms of invariance of the corresponding transfer function space to a given transformation in a Hilbert space, in a same way as the time invariance property for linear systems is related to the shift-invariance of the Hardy spaces. The transformation in question is exactly that defining the de Branges homogeneous spaces. The explicit form of the corresponding impulse response, which is shown to be described by a hyperbolic partial differential equation, is given.
منابع مشابه
Reproducing Kernel Hilbert Space Methods for Wide - Sense Self - Similar Processes
It has recently been observed that wide-sense self-similar processes have a rich linear structure analogous to that of wide-sense stationary processes. In this paper, a reproducing kernel Hilbert space (RKHS) approach is used to characterize this structure. The RKHS associated with a selfsimilar process on a variety of simple index sets has a straightforward description, provided that the scale...
متن کاملAn extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...
متن کاملSelf-similar solutions of the Riemann problem for two-dimensional systems of conservation laws
In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
متن کاملCompact Hilbert Indices
Space-filling curves are continuous self-similar functions which map compact multi-dimensional sets into one-dimensional ones. Since their invention they have found applications in a wide variety of fields [12, 21]. In the context of scientific computing and database systems, spacefilling curves can significantly improve data reuse and request times because of their locality properties [9, 13, ...
متن کاملApproximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces
This paper introduces an implicit scheme for a continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup. The main result is to prove the strong convergence of the proposed implicit scheme to the unique solutio...
متن کامل