Sentence examples for valid for functions from inspiring English sources

These definitions are valid for functions defined for and, respectively.

The limit Friedrichs-type inequality is valid for functions in the Sobolev space H1.

The convolution theorem will be valid for functions (F_{1}) representing linear sums of functions of the form (t^{mu }).

(2) Unfortunately, this result is no more valid for functions attaining their values in more general metric spaces.

The original version is valid for functions of finite order, and it was generalized to hold for meromorphic functions with hyper-order less than one recently.

Note that solutions of the limit problem (3) belong to W. We remark that an inequality of the form (6) cannot be valid for functions in W. Indeed, Proposition 2 There is no C > 0 such that the inequality ∫ Ω u 2 d x ≤ C ∫ Ω | ∇ u | 2 d x (8).

However, Theorem A does not remain valid for meromorphic functions.

Theorem 2.1 is still valid for convex functions.

The limit inequality is valid for all functions in the Sobolev space H1.

Heittokangas et al. [9], prove the following result which is a shifted analogue of Brück conjecture valid for meromorphic functions.

Such assertions are contained in Lemmas 9 and 10 and it is important that they are valid for all functions in B ¯ and not only for solutions of problem (1), (2).