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Lasha Ephremidze Gigla Janashia Edem Lagvilava 《Journal of Fourier Analysis and Applications》2011,17(5):976-990
It is proved that if positive definite matrix functions (i.e. matrix spectral densities) S
n
, n=1,2,… , are convergent in the L
1-norm, ||Sn-S||L1? 0\|S_{n}-S\|_{L_{1}}\to 0, and ò02plogdetSn(eiq) dq?ò02plogdetS(eiq) dq\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S_{n}(e^{i\theta})\,d\theta\to\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S(e^{i\theta})\,d\theta, then the corresponding (canonical) spectral factors are convergent in L
2, ||S+n-S+||L2? 0\|S^{+}_{n}-S^{+}\|_{L_{2}}\to 0. The formulated logarithmic condition is easily seen to be necessary for the latter convergence to take place. 相似文献
2.
Lasha Ephremidze Gigla Janashia Edem Lagvilava 《Journal of Fourier Analysis and Applications》2009,15(1):124-127
A very short proof of the Fejér-Riesz lemma is presented in the matrix case.
相似文献
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An effective factorization and partial indices are found for a class of unitary matrix functions. 相似文献
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In this paper, recently published results on matrix spectral factorization is reviewed, and their connection to wavelet matrices is revealed. 相似文献
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