We show that every (continuous) faithful product system admits a (continuous) faithful nondegenerate representation. For Hilbert spaces this is equivalent to Arveson’s result that every Arveson system comes from an E0–semigroup. We point out that for Hilbert modules this is not so. As applications we show a C–algebra version of a result for von Neumann algebras due to Arveson and Kishimoto, and...

Two independently emerging time-frequency transformations in Civil Engineering, namely, the wavelet transform and empirical mode decomposition with Hilbert transform EMD+HT , are discussed in this study. Their application to a variety of nonstationary and nonlinear signals has achieved mixed results, with some comparative studies casting significant doubt on the wavelet’s suitability for such a...

The Hilbert transformation together with empirical mode decomposition (EMD) produces Hilbert spectrum (HS) which is a fine-resolution timefrequency (TF) representation of any nonlinear and non-stationary signal. A method of audio signal separation from stereo mixtures based on the spatial location of the sources is presented in this paper. The TF representation of the audio signal is obtained b...

Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G × G. These transforms have remarkable properties...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Olavi Nevanlinna Name of the publication Multicentric representation and von Neumann spectral sets Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series SCIENCE + TECHNOLOGY 11/2011 Field of research Mathematics Abstract We show how multicentric representatio...

This paper deals with mechanical fault diagnosis in three-phase induction machines from stator current measurements. According to machine models, mechanical faults lead to amplitude and/or phase modulations of the measured stator current with possibly time varying carrier frequency. The modulation diagnosis requires a univocal definition of the instantaneous phase and amplitude. This is perform...

We present a to following results in the constructive theory of operator algebras. A representation theorem for finite dimensional von Neumann-algebras. A representation theorem for normal functionals. The spectral measure is independent of the choice of the basis of the underlying Hilbert space. Finally, the double commutant theorem for finite von Neumann algebras and for Abelian von Neumann a...

We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to a Hilbert modular form under mild assumptions on the residual image. In particular, we do not assume the residual image satisfies the Taylor–Wiles hypothesis. Using this, we deduce that the localization and completion of the universal deformation ring for the r...