Sentence examples for systems of function from inspiring English sources

It is easy to verify that the systems of function (6) and (7) are biorthonormal on [ 0, 1 ].

Basis properties of some trigonometric systems and other systems of functions (Haar system, classical system of Legendre, etc).

It will be important for us to investigate the denseness of some particular systems of functions in the C α.

In this work we suggest a new approach to describe textural information in terms of redundant systems of functions.

With the approach of Carleman's formula and Joel H Shapiro's construction, we could construct dense systems of functions from which the chaos of the solution semigroup follows.

It is easy to verify that the systems of functions X k ( x ) and Y k ( x ), k = 0, 1, 2, …  , are biorthonormal on [ 0, 1 ].

Thus the system of functions is independent.

The monic orthogonal polynomials form an orthogonal system of functions.

Z is the sequence of Fourier coefficients on the trigonometric system of functions f.

Then for every there exists a unique system of functions such that (2.7).

end{aligned} (28) Therefore, the system of functions (22) exists and is smooth.