M.I.T. Press, 1966. First edition in English.
Hardcover. Gray cloth, black spine lettering, tall octavo, xii, 353 pages.
Translated from the 1964 Russian original.

Very scarce monograph.

The monograph is devoted to a systematic exposition of the fundamentals of the theory of single sheeted domains of holomorphy and its applications to quantum field theory, to the theory of functions , and to differential equations with constant coefficients.
One of the first modern monographs on the theory of several complex variables, being different from other ones of the same period due to the extensive use of generalized functions.

This is the first work in English to provide a comprehensive and rigorous account of an area of active recent research, in which a number of fundamental results have been obtained – and applied – not only by pure mathematicians but also by theoretical physicists investigating the quantum field. Heretofore, these results have been scattered piecemeal in periodicals, and the subject has been treated by parts in the monograph literature. This detailed presentation represents a compilation of these sources and, more than that, provides a systematic development of this complex field. Indeed, it has brought a vigorous and rapidly unfolded domain of study to formal maturity with an uncommon dispatch.

The careful presentation of preliminaries and the self-contained exposition of homology will be especially serviceable to the physicists, in whose hands this mathematical formalism should become a convenient and powerful tool for prying into the quantum realm. The author provides explicit applications of holomprphic functions to quantum field theory and to different equations with constant coefficients, among other subjects.

Vasily Sergeyevich Vladimirov (9 January 1923 – 3 November 2012) was a Soviet and Russian mathematician working in the fields of number theory, mathematical physics, quantum field theory, numerical analysis, generalized functions, several complex variables, p-adic analysis, multidimensional Tauberian theorems.

As the Soviet atomic bomb programme ran, Vladimirov was assigned to assist with the development of the bomb, in joint force with many top scientists and industrialists. He worked with Vitalevich Kantorovich calculating critical parameters of certain simple nuclear systems. In 1950, when he was sent to Arzamas-16, he worked under the direction of Nikolai Nikolaevich Bogolyubov, who later became a long-term collaborator with Vladimirov. In Arzamas-16, Vladimirov worked on finding mathematical solutions for problems raised by physicists. He developed new techniques for the numerical solution of boundary value problems, especially for solving the kinetic equation of neutron transfer in nuclear reactors in 1952, which is now known as Vladimirov method.

After the success of the bomb project, Vladimirov was awarded the Stalin Prize in for his contribution 1953. He continued working on mathematics for atomic bomb in the Central Scientific Research Institute for Artillery Armaments, where he served as Senior Researcher in 1955. Vladimirov moved to Steklov Mathematical Institute, Moscow, in 1956, under the supervision of Nikolay Nikolaevich Bogolyubov.[1] There he started working on new mathematical branches for solving problems in quantum field theory. He defended his doctoral thesis in 1958, which contains the renowned 'Vladimirov variational principle'.

CONDITION: Fine book in Near Fine dust jacket. (Book has small price notation at top of front endpaper. Dust jacket has light wear at tiop of spine, archival tape repair long one fold.)