Operators extended norm operator

When NORM is brought to the surface, it remains in the rock pieces of the drill cuttings, remains in solution with produced water, or, under certain conditions, precipitates out in scales or sludge. The radiation from this NORM is weak and cannot penetrate dense materials such as the steel used in pipes and tanks (Smith et al., 1996). The principal concern for NORM in the oil and gas industry is that, over time, it can become concentrated in field production equipment (API, 2004) and as sludge or sediment inside tanks and process vessels that have an extended history of contact with formation water (BSEEC, 2012). Because the general public does not come into contact with oilfield equipment for extended periods, there is little exposure risk from oilfield NORM. Studies have shown that exposure risks for workers and the public are low for conventional oil and gas operations (BSEEC, 2012 Smith et al., 1996). 

If f(t) is an energy signal, then we can consider f(t) as belonging to the Hilbert space, L2(R)- The reader unfamiliar with Hilbert space may think of it as a generalisation of the three-dimensional Euclidean space, in which the concepts of distance and angle are extended as norm and inner product respectively. For any signal in the Hilbert space, it has the basic operation properties that can be added, subtracted and multiplied by constants. 

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