Product Description
This volume, the eighth out of nine, continues the translation of "Treatise on Analysis" by the French author and mathematician, Jean Dieudonne. The author shows how, for a voluntary restricted class of linear partial differential equations, the use of Lax/Maslov operators and pseudodifferential operators, combined with the spectral theory of operators in Hilbert spaces, leads to solutions that are much more explicit than solutions arrived at through "a priori" inequalities, which are useless applications. ... Read more

Customer Reviews (2)

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THE ATOMIC NUCLEUS IT'S ABSTRACT!!!

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MAURICE ALLMAN L

Abstraction to its last consequences.
I should be surprised to be the first reviewer of this book, but thinking it again I see the point. Dieudonné's books are just being displaced by more accesible and focused texts, instead of these authoritativeBourbaki-style treatises which are often too abstract to be useful.Bourbaki mathematics accomplished the mission of unifying and standarizing(more or less) the whole of mathematics, but once that was done, their worknow turns out to be useless. The point is that when we tackle a problem, beit in pure or applied mathematics, we seldom need the high level ofabstraction used by Bourbaki authors. Moreover, what we need are specificresults to handle the details of our solututions, and Dieudonné pays almostno attention to them; he prefers to stay at the most general possiblesetting, making his treatment perspectiveless because he misses completelythe goal of abstraction: To use its power when dealing with particularsituations. That's why no one has reviewed Dieudonné before me: His booksare read no more.

Nevertheless, undergraduate and graduate students mayfind it useful as a reference, but not as a course text because it presentsno motivation to the topics treated and includes only a very shortbibliography.

Its contents are: Set theory, real numbers, metric spaces,normed spaces, Hilbert spaces, spaces of continuous functions, differentialcalculus, analytic functions, existence theorems (for ODE's), andelementary spectral theory.

"Treatise on Analysis" consistedoriginally on this sole book. Later it was expanded to four and later on tonine. ... Read more

Product Description
High Quality Content by WIKIPEDIA articles! The X-machine (XM) is a theoretical model of computation introduced by Samuel Eilenberg in 1974. The X in "X-machine" represents the fundamental data type on which the machine operates; for example, a machine that operates on databases (objects of type database) would be a database-machine. The X-machine model is structurally the same as the finite state machine, except that the symbols used to label the machine's transitions denote relations of type X?X. Crossing a transition is equivalent to applying the relation that labels it (computing a set of changes to the data type X), and traversing a path in the machine corresponds to applying all the associated relations, one after the other. ... Read more