Geodesic
Harmonic analysis of cosine and exponential operator-valued functions
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 63-90

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This article concerns: 1) theorems on the spectra of operators formed from cosine operator-valued functions and representations; 2) inequalities (of Bernstein type) connecting the norms of operators with their spectral radii; 3) applications to second-order differential equations; 4) generalizations of the known spectral criterion of Loomis for almost periodicity, and an application to the investigation of almost periodicity of cosine operator-valued functions, representations, and solutions of functional equations; and 5) linear methods for summation of Fourier series in eigenfunctions of a linear operator generating a bounded (one-parameter) cosine operator-valued function. Bibliography: 41 titles. 
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     author = {A. G. Baskakov},
     title = {Harmonic analysis of cosine and exponential operator-valued functions},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_1_a4/}
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A. G. Baskakov. Harmonic analysis of cosine and exponential operator-valued functions. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 63-90. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a4/