In some applications of a CS in the context of a spatial reference frame (see Clause 8), it is necessary to consider a displaced and/or rotated version of a CS. To consider such a CS, a generating function for the displaced and rotated version of the CS must be specified. These modified versions of CS generating functions may be specified in a uniform way through the process of localization defined below.
Three parameterized operators, called localization operators, that operate on or between position-spaces are defined in Table 5 .2 and the inverses of these operators are specified in Table 5 .3.
Table 5.2 — Localization operators
Localization
operator
|
Domain
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Range
|
Localization parameters
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Operator definition
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|
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q, r, s, in
r and s are orthonormal
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