During the past decade there have been many changes in the perfumery industry which are not so much due to the discovery and application of new raw materials, but rather to the astronomic increase in the cost of labour required to produce them. This is reflected more particularly in the flower industry, where the cost of collecting the blossoms delivered to the factories has gone up year after year, so much so that most flowers with the possible exception of Mimosa, have reached a cost price which has compelled the perfumer to either reduce his purchases of absolutes and concretes, or alternatively to substitute them from a cheaper source, or even to discontinue their use. This development raises an important and almost insoluble problem for the perfumer, who is faced with the necessity of trying to keep unchanged the bouquet of his fragrances, and moreover, to ensure no loss of strength and diffusiveness. Of course, this problem applies more especially to the adjustment of formulae for established perfumes, because in every new creation the present high cost of raw materials receives imperative con- sideration before the formula is approved.
This is a unique book related to the theory of functions of a-bounded type in the half-plane of the complex plane, which is constructed by application of the Liouville integro-differential operator.
In addition, the book contains improvements of several results such as the Phragmen-Lindelof Principle and Nevanlinna Factorization in the Half-Plane, and offers a new, equivalent definition of the classical Hardy spaces in the half-plane.
The last chapter of the book presents an application of the constructed theory as well as M.M.Djrbashiana (TM)s theory of Nevanlinna type classes in the disc in the spectral theory of linear operators. This is a solution of a problem repeatedly stated by M.G.Krein and being of special interest for a long time.
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