absolutely integrable造句

• The diffeomorphism group are flows with vector fields absolutely integrable in Sobolev norm
• The diffeomorphism group are flows with vector fields absolutely integrable in Sobolev norm:
• Provided that \ gamma ( \ tau ) is absolutely integrable ( which is not always true ),
• These conditions have the benefit that the integrals that define the Fourier transform and its inverse are absolutely integrable.
• Nor is r _ { xx } assumed to be absolutely integrable, so it need not have a Fourier transform, either.
• The Fourier inversion theorem holds for all continuous functions that are absolutely integrable ( i . e . ) with absolutely integrable Fourier transform.
• The Fourier inversion theorem holds for all continuous functions that are absolutely integrable ( i . e . ) with absolutely integrable Fourier transform.
• A slight variant is to drop the condition that the function be continuous but still require that it and its Fourier transform are absolutely integrable.
• However, the hypothesis that f is measurable is crucial; it is not generally true that absolutely integrable functions on [ a, b ] are integrable.
• If the function is absolutely integrable in one dimension ( i . e . ) and is piecewise smooth then a version of the Fourier inversion theorem holds.
• If the function is absolutely integrable in one dimension ( i . e . ) but merely piecewise continuous then a version of the Fourier inversion theorem still holds.
• If we drop all assumptions about the ( piecewise ) continuity of and assume merely that it is absolutely integrable, then a version of the theorem still holds.
• To allow it to take +  " as a value, one needs to replace the assumption about " f " being absolutely integrable with the more relaxed condition
• Note that the Fourier transform of x ( t ) \, does not exist in general, because stationary random functions are not generally either square integrable or absolutely integrable.
• An absolutely integrable function for which Fourier inversion holds good can be expanded in terms of genuine frequencies ( avoiding negative frequencies, which are sometimes considered hard to interpret physically ) by
• Note that one may need to require f to be absolutely integrable with respect to the weight w ( x ) \, dx in order for this integral to be finite.
• If is continuous and absolutely integrable on then the Fourier inversion theorem still holds so long as we again define the inverse transform with a smooth cut off function i . e.
• Although using the Fourier transform, it is easy to see that this generates a semigroup in some sense, it is not absolutely integrable and so cannot define a semigroup in the above strong sense.
• This condition has the benefit that it is an elementary direct statement about the function ( as opposed to imposing a condition on its Fourier transform ), and the integral that defines the Fourier transform and its inverse are absolutely integrable.
• The authors go on to extend the integral still further in Section 13 ( Absolutely Integrable Functions ), and at this point I have no idea at all how this integration theory compares in power and scope to the likes of the Lebesgue approach.