We prove that there exists a unique Hubert space of holomorphic functions in the open unit ball of C" whose (semi-) inner product is invariant under Möbius transformations.

An algorithm is given for the computation of moments of f 2 S, where S is either a principal h-shift invariant space or S is a nitely generated h-shift invariant space. An error estimate for the rate of convergence of our scheme is also presented. In so doing, we obtain a result for computing inner products in these spaces. As corollaries, we derive Marsden-type identities for principal h-shift...

Introduction: Sensorineural hearing loss (SNHL) is one of the possible complications of radiotherapy treatment of brain tumors. The auditory system of patients with brain tumors often is placed inside of radiation field and receives a significant amount of radiation dose resulting in hearing loss. The purpose of this study was to compare contouring and delivery dose to cochlea...

We consider the efficient quantization of a class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. By definition, these signals are cwersampled and it is reasonable to expect that we can reap the same benefits of well known efficient A/D conversion techniques. Indeed, by using appropriate multirate reconstruction schemes, ...

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model p...

In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risksensitive filter asymptotically converges to any suboptimal filter initialized wit...

Lars Lindbom, Mikael Sternad and Anders Ahlén Signals and Systems, Uppsala University, PO Box 528, SE-75120, Uppsala, Sweden. [email protected], ms,aa @signal.uu.se Abstract: Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member. Closed-form expressions for the tracking MSE...

We connect shift-invariant characteristic kernels to infinitely divisible distributions on R. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is twofold. First, we show, using the Lévy–Khintchine formula, that any shift-invariant kernel given by a bounded, continuou...

Approximations of slightly nonlinear systems with linear time-invariant (LTI) models are often used in applications. Here, LTI models that are optimal approximations in the mean-square error sense are studied. It is shown that these models can be very sensitive to small nonlinearities. Furthermore, the significance of the distribution of the input process is discussed. From the examples studied...

In this paper, we study asymptotic stability properties of risk-sensitive lters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risk-sensitive lter asymptotically converges to any suboptimal lter initialized with an ...