Sentence examples for square-integrable function from inspiring English sources

First, under the same type of conditions as for the Shannon theorem, the scaling coefficients of a wavelet expansion will determine uniquely the given square-integrable function.

Assume that (v(x)) is a square-integrable function with respect to the shifted Legendre weight function.

The cumulative of a square-integrable function with a single bump would have these properties, and a Gaussian is arguably the simplest choice.

Here the control input g ( t ) is a function of time t; the problem considers any square-integrable function for g ( t ).

Knowing that the spherical harmonics form a complete orthonormal basis over allows the expansion of any square-integrable function (i.e., vMF) as a linear combination of these (4).

end{aligned} (32) Now, suppose that (f(x)) is an arbitrary square-integrable function on the intervals (Omega_{i}) ((i=1,2,ldots,n+1)).

When the Hilbert space is the space L2(D) of square-integrable functions on a domain D, the quantity: :\varphi_n \varphi_n^\dagger, is an integral operator, and the expression for f can be rewritten as: :f(x) = \sum_{n=1}^\infty \int_D\, \left( \varphi_n (x) \varphi_n^*(\xi \right) f(\xi) \, d \xi.

Let L2 be the Lebesgue space of square-integrable functions on the unit circle.

We construct a family of irreducible unitary representations of the loop affine group of a line (ax+b group) with central extension on the Hilbert space of square-integrable functions with respect to the Wiener measure.

He began with the space of square-integrable functions on the real line.

We denote the space of square-integrable functions over (Omega = -1,1)) by (L^{2}(Omega)).