essentially bounded function

essentially bounded function

[i¦sen·chə·lē ¦bau̇nd·əd ′fəŋk·shən]
(mathematics)
A function that has an essential bound.
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Now let us introduce the concept of a generalized factorization for matrix functions (see, for instance, [14] and [42]): we say that a matrix function r [member of] [[[L.sub.[infinity]](T)].sub.n,n], that is, a matrix function whose entries are essentially bounded functions on the curve T, admits a left (right) generalized factorization in [L.sub.2]( T) if it can be represented as