Those with the original 1967 edition of this classic on their bookshelves keep their office doors locked. Tréves (mathematics, Rutgers U.) wrote this for upper-level undergraduates and early graduate students as they studied functional analysis as well as the analysis relevant to the solutions of partial differential equations, an expansion that has proved invaluable to a couple of generations of mathematicians, engineers and other scientists. Along with the astounding 390 exercises, Tréves fully topological vector spaces and spaces of function, with forays into Cauchy filters and Fréchet spaces, Hilbert spaces and partitions of unity, then moves to duality and spaces of distribution with radon measures, the continuous linear map and Sobolev spaces, then into tensor products and kernals, which includes very interesting commentary on nuclear mapping. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)