We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous 2-cocycle one associates the reduced C∗-algebra. Elements (or multipliers) of this algebra admit natural Hilbert space representations. show relevance orbit closure structure unit in dealing spectra, norms, numerical ranges and ε-pseudospectra resulting operators. As an examp...

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

Hidden Markov modeling of speech waveforms is studied and applied to speech recognition of clean and noisy signals. Signal vectors in each state are assumed Gaussian with zero mean and a Toeplitz covariance matrix. This model allows short signal vectors and thus is useful for speech signals with rapidly changing second order statistics. It can also be straightforwardly adapted to noisy signals ...

Szegö’s theorem states that the asymptotic behavior of the eigenvalues of a Hermitian Toeplitz matrix is linked to the Fourier transform of its entries. This result was later extended to block Toeplitz matrices, i.e., covariance matrices of multivariate stationary processes. The present work gives a new proof of Szegö’s theorem applied to block Toeplitz matrices. We focus on a particular class ...

We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that these matrices are expected to be very well conditioned. Our probabilistic estimates for the norms of standard Gaussian random Toeplit...

The minimum variance (MV) spectral estimator is a robust high-resolution frequencydomain analysis tool for short data records. The traditional formulation of the minimum variance spectral estimation (MVSE) depends on the inverse of a Toeplitz autocorrelation matrix, for which a fast computational algorithm exists that exploits this structure. This paper extends the MVSE approach to two data-onl...

We consider the solutions of Hermitian Toeplitz systems where the Toeplitz matrices are generated by nonnegative functions f. The preconditioned conjugate gradient method with well-known circulant preconditioners fails in the case when f has zeros. In this paper, we employ Toeplitz matrices of xed band-width as preconditioners. Their generating functions g are trigonometric poly-nomials of xed ...

In this article we derive, using standard methods of Toeplitz theory, an asymptotic formula for certain large minors of Toeplitz matrices. Bump and Diaconis obtained the same asymptotics using representation theory, with an answer having a different form.

In this paper, the Fredholm properties of some Toeplitz operators on Dirichlet spaces be discussed, and the essential spectra of Toeplitz operators with symbols in C 1 or H ∞ 1 + C 1 be computed.