Displaying similar documents to “Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem.”

A spectral characterization of the behavior of discrete time AR–representations over a finite time interval

E. N. Antoniou, Antonis I. G. Vardulakis, Nikolas P. Karampetakis (1998)

Kybernetika

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In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.

A new bound for the spectral radius of Brualdi-Li matrices

Xiaogen Chen (2015)

Special Matrices

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Let B2m denote the Brualdi-Li matrix of order 2m, and let ρ2m = ρ(B2m ) denote the spectral radius of the Brualdi-Li Matrix. Then [...] . where m > 2, e = 2.71828 · · · , [...] and [...] .

The Direct and Inverse Spectral Problems for some Banded Matrices

Zagorodnyuk, S. M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.

Initial boundary value problem for the mKdV equation on a finite interval

Anne Boutet de Monvel, Dmitry Shepelsky (2004)

Annales de l’institut Fourier

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We analyse an initial-boundary value problem for the mKdV equation on a finite interval ( 0 , L ) by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex k -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at t = 0 and x = 0 , L . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms...