integrable function

(redirected from Square integrable)

integrable function

[¦int·i·grə·bəl ′fəŋk·shən]
(mathematics)
A function whose integral, defined in a specific manner, exists and is finite.
References in periodicals archive ?
2][0, [infinity]) denote the set of all real-valued functions h that are square integrable on [0, [infinity]), i.
The first one presented in Section 3 treats a fuzzy equation as an abstract relation in the metric space of fuzzy sets over the space of square integrable random vectors.
The convolution is used for the definition of discontinuous bases of the space of square integrable functions whose elements are as close to a classical orthonormal system as desired.
0]([OMEGA]) denotes the space of Sobolev functions which are square integrable up to their weak first-order derivatives and which have zero boundary values in the sense of traces.
For any square integrable function x on [-1, 1], we define the function
A more general definition of window functions does not require them to be identically zero outside an interval, as long as the product of the window multiplied by its argument is square integrable, that is, that the function goes sufficiently rapidly toward zero.
Equation (2) means that the only a priori information about the magnetic current is that it is a square integrable function defined on the source domain S whereas the radiated field is assumed as a square integrable function defined on the measurement domain [O.
2](X,v) be the Hilbert space of square integrable functions on X with respect to the marginal measure v.
Next, we want to show that [psi] is square integrable on the real line (1).
In this paper the authors prove that a square integrable function f on I[R.
t]-adapted random processes having square integrable norms (with respect to the measure P) which are bounded on I.