The phrase "author extends" is correct and usable in written English.
It can be used when discussing the actions or contributions of an author, particularly in the context of expanding on ideas or concepts in their work.
Example: "In this chapter, the author extends the discussion on climate change by introducing new research findings."
Alternatives: "the author elaborates" or "the author expands".
The author extends an improved structure of feedback neural network to formulate the error function in the optimization of QMF banks as a Lyapunov energy function to find the Hopfield-related parameters.
It falters only when the author extends too far beyond this narrative, imagining a bit too colorfully village life in Zakho or obsessively self-analyzing his dissonant relationship with his father.
In [6], the author extends the results in [1], [2] under the general asymptotically linear condition.
In this paper, the author extends the results in (Qin et al. in J. Differ. Equ. 253:1439-1488, 2012).
The author extends his appreciation to the OECD for its support through the T.J. Alexander Fellowship, as well as its hospitality at the initiation of this work.
In this book the author extends the concepts previously introduced in his "Quantum Field Theory in Condensed Matter Physics" to situations in which the strong electronic correlations are crucial for the understanding of the observed phenomena.
Therefore, the author extended MLP to E-Governance systems by considering both approaches of evolution.
Tl e shales described by the author extend from about three miles S.W. of Carnarvon to Bangor, running nearly parallel to the Menai Straits.
The author extended the CAV (U) Theorem of Aumaan Maschler (Aumann et al. 1995).
Thus the author extended the well-known notions of discrete and smooth pseudospherical surfaces.
In [1], the first author extended Theorem to a real uniformly smooth Banach space and proved the following theorem.
