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Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other.
The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).
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Michael Waltenburg
reviewed Asymptotic theory of finite dimensional normed spaces on April 23, 2014 Asymptotic theory of finite dimensional normed spaces
I often disagree with historians, but John Evangelist Walsh is one of the very, very few that makes me genuinely angry. His incomprehensibly long career has been built on promoting demonstrably fictitious and horribly libelous claims against historical figures. Poe has been one of his main victims. Walsh's previous book, "Plumes in the Dust," made the lunatic, completely unsubstantiated claim that Poe fathered an illegitimate child on a married woman. In "Midnight Dreary" he piles fantasy on fantasy by suggesting that Poe was murdered by two (possibly imaginary) brothers of a woman he may have planned to marry.
As is usual with Walsh, there is absolutely no evidence to support his thesis. His M.O. is to dream up a headline-grabbing, lurid scenario. Then, he proceeds to write a work of fiction to gull the unwary into thinking he has a case. He manipulates or simply invents "evidence" for whatever half-baked idea he is promoting, while completely ignoring the usually vast amount of documentation that would utterly destroy his story. He is an expert at dreaming up fictitious scenarios and invented conversations, and then using his own creations as support!
"Midnight Dreary" is only one of his many rather frightening distorions of history. Poe scholars have long treated Walsh as a bad joke, but it is depressing to think how many readers who don't know the facts will be lured by Walsh's air of authority and pseudo-scholarship into thinking his books have any credibility. This is not history--it is a bad hoax. I have my doubts whether Walsh himself belives any of the defamatory drivel he puts out at such an alarming rate.
P.S. For a more detailed analysis of Walsh's pernicious methods here is an Emily Dickinson scholar reviewing (with great disgust) Walsh's recent "book" about the Amherst poet:
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