Abstract
In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach, which include Webb’s [1] and Shaw’s [2] formulae and some new one as special cases. We also give the quantitative estimations for the general formulae.
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References
Webb, G.F., A Representation Formula for Strongly Continuous Cosine Families, Aequationes Math. 21 (1980), 251–256
Shaw S-Y, Lee C-S and Chiou W-L, Representation Formulas for Cosine and Sine Functions of Operators, Aequationes Math. 31 (1986), 64–75.
Lutz, D., Strongly Continuous Cosine Functions, “Functional Analysis Lecture Note in Mathematics 948”, Springer Berlin (1982), 72–97.
Fattorini, H. O., Ordinary Differential Equations in Linear Topological Spaces, I., J. Differential Equations 5(1969), 72–105
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Mi, Z., Wenzhong, C. The probabilistic representation formulae for cosine operator functions. Approx. Theory & its Appl. 9, 42–52 (1993). https://doi.org/10.1007/BF02836150
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DOI: https://doi.org/10.1007/BF02836150