Toeplitz Forms And Their Applications

By U. Grenander, G. Szegő, M. Kac. 1958

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “, 2009; Gray, 2006) (Grenander and Szego, 1958) EdE ITE: Shannon Edgeworth (van Hulle, 2005) Gau based on (9) ME1 ITE: Shannon MaxEnt1 (Hyvärinen, 1997) ME2 ITE: Shannon MaxEnt2 (Hyvärinen, 1997)”
SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS (2019, unknown): “The following lemma is due to Carath´eodory (see, for example, [8]).”
Performance of some variable selection methods when multicollinearity is present (2005, background): “(8) gives a very specific pattern to the eigenvalues and eigenvectors of G [10].”
On the Interdependence of Routing and Data Compression in Multi-Hop Sensor Networks (2002, background): “Szegö’s theorem [7] establishes that asymptotically the eigenvalues of a Toeplitz matrix converge to the spectrum of the correlation function.”
On the capacity of OFDM-based spatial multiplexing systems (2002, methodology): “We can thus invoke Szegö’s theorem [24] to obtain the limiting distribution 6 of the eigenvalues of as Using (5), we obtain (17) with the third-order theta function given by [25] .”
A note on a Marčenko–Pastur type theorem for time series (2011, background): “Further refinements are made successively by many researchers including Jonsson (1982), Wachter (1978) and Yin (1986). An important work by Silverstein (1995) aimed at relaxing the independence structure between the coordinates of the Xj ’s and considered random vectors of form Yj = T 1/2 p Xj where”
Determining the Number of Factors from Empirical Distribution of Eigenvalues (2010, unknown): “It is easy to show that V (k) and ^ �2 in ( 18 ),(19), and (20)”
The GLT class as a generalized Fourier analysis and applications (2006, background): “[15,96,18,97,98,4,60,66,67,87,69,86,88,91], is a famous theorem of Szegö [35], which we report in the Tyrtyshnikov and Zamarashkin version [93]:”
Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator (2018, unknown): “(see [17]) If the function p ∈ P is defined by p (z) = 1 + p1z + p2z(2) + p3z(3) + · · · , then 2p2 = p(2)1 + ξ ( 4 − p(2)1 )”
Entropy and Kullback-Leibler divergence estimation based on Szegö's theorem (2009, methodology): “In this subsection, we review the Szegö's theorem for sequences of Toeplitz matrices [12] [13] r[−1] · · · r[−K + 1] r[1] r[0] · · · r[−K + 2] . . . . . . . . . . .”
Sure independence screening for ultrahigh dimensional feature space (2006, background): “See also Grenander and Szeg¨o (1984) for more details on the characterization of extreme eigenvalues of the covariance matrix of a stationary process in terms of its spectral density.”