Beiträge zur Theorie der Toeplitzschen Formen

Abstract

Unter To'eplitzschen Formen verstehe ich diejenigen Hermite-So gehSrt zu jeder Funktion f(O) eine ganz bestimmte Schar yon Toeplitzschen Formen ~)

On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators

“…The literature is vast on spectral approximation and we can only refer to a subset here. For selected papers and books we consider to be important and related to the topic of this paper we refer to [9,11,10,26,32,15,14,41,19,18,28,42,47] for a functional analysis exposition and [50,48,25,39] for a more applied mathematical treatment.…”

Competitive principal component analysis for locally stationary time series

“…Szegö [23] showed that the eigenvalues are asymptotically equal to the power spectrum sampled at equal frequency intervals. To illustrate this in the infinite case, consider the Fourier transform of the eigenvalue equation (4) (9) where power spectrum associated with the input signal autocorrelation function; Fourier transform of the th eigenfilter; eigenfilter dimension as defined previously.…”

“…The free parameters of the MOE system to be determined, for competitive linear PCA, are the weights of the gating and expert networks. Following Weigend [25], the total likelihood over the entire data set is given by (23) where, under the assumption that only one expert is valid at a given time, the binary indicator variable , indicating which expert is valid, allowed us to replace the sum of the likelihoods over the experts by a product. The indicator variable is "missing" in the sense that we do not know a priori which expert is valid at any time step.…”

Localização dos zeros de polinômios de Szegö com coeficientes de reflexão maiores que um em módulo

“…Com as publicações [15] e [16], no início do século XX, Szegő introduziu os polinômios ortogonais no círculo unitário, também chamados de polinômios de Szegő em sua homenagem. Os polinômios de Szegő podem ser definidos e estudados em termos de funcionais de momento, da seguinte forma:…”