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On the singularity of the spectral measures of a semi-infinite random system. (English) Zbl 0295.47031


MSC:

47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A10 Spectrum, resolvent
60H99 Stochastic analysis
60J60 Diffusion processes
60G30 Continuity and singularity of induced measures
39A10 Additive difference equations
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References:

[1] H. Matsuda and K. Ishii: Localization of normal mode and energy transport in the disordered harmonic chain. Prog. Theor. Phys. Suppl., 45, 56-86 (1970).
[2] K. Ishii: Localization of eigenstates and transport phenomena in the one dimensional disordered system (to appear in Prog. Theor. Phys. Suppl.). · Zbl 0711.54019
[3] A. Casher and J. L. Lebowitz: Heat flow in regular and disordered harmonic chains. J. Math. Phys., 12(8), 1701-1711 (1971).
[4] H. Furstenberg: Non commuting random products. Trans. Amer. Math. Soc, 108, 377-428 (1963). JSTOR: · Zbl 0203.19102
[5] N. I. Akhiezer: The Classical Moment Problem. Oliver & Boyd Ltd. (1965). · Zbl 0173.41001
[6] H. Wall: Analytic Theory of Continued Fractions. Chelsea. Publ. Comp. (1948). · Zbl 0035.03601
[7] K. Hoffman: Banach Spaces of Analytic Functions. Prentice-Hall (1965). · Zbl 0117.34001
[8] T. Asahi and S. Kashiwamura: Spectral theory of the difference equations in isotopically disordered harmonic chains. Prog. Theor. Phys., 48, 361-371 (1972). · Zbl 1098.82501
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