Abstract
The analytical theory of semi-groups of bounded linear operators in a B-space deals with the exponential functions in infinite dimensional function spaces. It is concerned with the problem of determining the most general bounded linear operator valued function T (t), t ≧ 0, which satisfies the equations
The problem was investigated by E. Hille [2] and K. Yosida [5] independently of each other around 1948. They introduced the notion of the infinitesimal generator A of T (t) defined by
and discussed the generation of T (t) in terms of A and obtained a characterization of the infinitesimal generator A in terms of the spectral property of A.
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© 1968 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1968). Analytical Theory of Semi-groups. In: Functional Analysis. Die Grundlehren der mathematischen Wissenschaften, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11791-0_10
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DOI: https://doi.org/10.1007/978-3-662-11791-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11793-4
Online ISBN: 978-3-662-11791-0
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