Sentence examples for basic results that will from inspiring English sources

For the convenience of the reader, we present some definitions, lemmas, and basic results that will be used later.

In this section we recall some basic results that will be used in this paper and also fix some notations.

First, we recollect some fundamental definitions and notations and basic results that will be used throughout this paper.

In this section, we present some definitions, lemmas, and basic results that will be used in the article.

For convenience of the reader, we present here some definitions, lemmas, and basic results that will be used in the proofs of our theorems.

Let I denote the identity operator on H. Next, we recall several definitions and basic results that will be available later.

Now, we present basic definitions and results that will be needed in the rest of the paper.

For the sake of simplicity for the reader, we recall here more basic notions and results that will be needed in the sequel, see [11] for more details.

For convenience of the readers, we first present some basic notation and results that will be used in the proofs of our theorems.

We now recollect some basic definitions, notations, and results that will be used subsequently.

We begin this section by presenting basic definitions and preliminary results that will be used throughout the paper.