In this post, we will see the book Linear Differential Operators: Part 1 – Elementary Theory of Linear Differential Operators by M. A. Naimark.

About the book

In the present book, the theory of linear, ordinary, differential operators of arbitrary order is developed. Extensive use is made of the ideas and theorems of functional analysis, especially those of the theory of linear operators in Hilbert space. For the reader’s convenience all the necessary theorems in functional analysis are developed in the text itself, to make the book, as the author hopes, self-contained and accessible to a wide range of readers-. Many topics in the theory oflinear differential operators can also be discussed without using functional analysis, as Titchmarsh’s treatment [112a] shows. However, the author does not consider such a treatment to be appropriate, since it is only by using the ideas and methods of functional analysis that a deeper understanding of the theory, and its most general results, can be achieved.

The book is in two parts. In the first part, which may be described as an elementary theory of differential operators, the use of the methods of functional analysis is kept to a minimum. This part presents the theory of differential operators defined on a finite interval, including the case of differential opera­ tors which are not self-adjoint, the theory being developed on the assumption that the coefficients of the operators are sufficiently smooth, i.e., sufficiently differentiable. To understand Part I the reader needs only an elementary know­ ledge of the theory of ordinary differential and integral equations and of the theory of functions.

Part II develops the theory of differential operators, using Hilbert space methods. Here, in addition to the subjects already mentioned, the reader will be expected to have some knowledge of the basic results in the theory of the Lebesgue integral.

You can get the book here.
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