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Displaying 21 – 27 of 27

Convergence of series of dilated functions and spectral norms of GCD matrices

Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber (2015)

Acta Arithmetica

We establish a connection between the L² norm of sums of dilated functions whose jth Fourier coefficients are $(j^{- α})$ for some α ∈ (1/2,1), and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in L² and for the almost everywhere convergence of series of dilated functions.

Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem.

Freitag, Melina A., Spence, Alastair (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Convex $SO (N) \times SO (n)$ -invariant functions and refinements of von Neumann’s inequality

Bernard Dacorogna, Pierre Maréchal (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

A function $f$ on $M_{N \times n} (ℝ)$ which is $SO (N) \times SO (n)$ -invariant is convex if and only if its restriction to the subspace of diagonal matrices is convex. This results from Von Neumann type inequalities and appeals, in the case where $N = n$ , to the notion of signed singular value.

Correction to "Generalized approximation numbers" (Port. Math., 43(1) (1985-1986), 157-166)

Queiró, João Filipe (1988)

Portugaliae mathematica

Correction to my paper: “On pairs of matrices with property $L$ ”

Jiří Kopáček (1972)

Commentationes Mathematicae Universitatis Carolinae

Covariance Structure of Principal Components for Three-Part Compositional Data

Klára Hrůzová, Karel Hron, Miroslav Rypka, Eva Fišerová (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates....

Criteria of unitary equivalence of Hermitian operators with a degenerate spectrum.

Lomidze, I. (1996)

Georgian Mathematical Journal

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