pointwise

Then we pointwise multiply the respective Fourier coefficients of the two polynomials, and finally we us an inverse FFT to return a polynomial of degree .

Suppose that 'f'n'′ are uniformly equicontinuous and uniformly bounded, and that the sequence 'f'n' is pointwise bounded (or just bounded at a single point).

For instance, if a set F is compact in C(X), the Banach space of real-valued continuous functions on a compact Hausdorff space with respect to its uniform norm, then it is bounded in the uniform norm on C(X) and in particular is pointwise bounded.

Usually the rank of a function is a pointwise property.

Next, set the pointwise limit of the sequence to be f.

The operations are pointwise addition and multiplication of functions.

In order theory it is common to define a pointwise partial order on functions.

It can be made into a preordered set itself by the pointwise relation:

Commands which operate on data in a pointwise manner cause no difficulty with this processing method.

The filters' amplitude responses are thus pointwise square roots of the system filters.

In 1975, Natterer proved pointwise convergence of finite element methods.

Obviously , thus is an eigenfunction of the pointwise function multiplication.

This kind of example belongs to the theory of real analysis where the pointwise value of functions matters.

In general, the most common criteria for pointwise convergence of a periodic function f are as follows:

In a pointwise estimator, the kernel width is varied depending on the location of the sample.

Univariate linear regression of pointwise visual field sensitivity against time of follow-up.

The nil-theta functions with pointwise multiplication on form a graded algebra (here ).

This is a pointwise prediction interval.

We have pointwise convergence, but not uniform convergence.

The pointwise maximum of two subharmonic functions is subharmonic.

The structure of algebra over the complex numbers is obtained by considering the pointwise operations of addition and multiplication.

Mergelyan also has many important results in other areas of complex analysis including the theory of pointwise approximations by polynomials.

MI is the expected value of the pointwise mutual information (PMI).

Indeed, it coincides with the topology of pointwise convergence of linear functionals.

The group operation in the external direct sum is pointwise multiplication, as in the usual direct product.

Considerable sensitivity to each of the four general surface energy balance extensions was identified in average pointwise monthly changes for important land-atmosphere interface variables.

Usually its multiplication is taken to be function composition, while its addition is pointwise addition of the images.

A proposal closely related to Prigogine's is that the pointwise rate of entropy production should have its maximum value minimized at the steady state.