By Peter Buser (auth.)
This vintage monograph is a self-contained creation to the geometry of Riemann surfaces of continuous curvature –1 and their size and eigenvalue spectra. It specializes in matters: the geometric concept of compact Riemann surfaces of genus more than one, and the connection of the Laplace operator with the geometry of such surfaces. the 1st a part of the booklet is written in textbook shape on the graduate point, with basically minimum specifications in both differential geometry or complicated Riemann floor thought. the second one a part of the ebook is a self-contained advent to the spectrum of the Laplacian in line with the warmth equation. Later chapters take care of fresh advancements on isospectrality, Sunada’s building, a simplified facts of Wolpert’s theorem, and an estimate of the variety of pairwise isospectral non-isometric examples which relies purely on genus. Researchers and graduate scholars attracted to compact Riemann surfaces will locate this booklet an invaluable reference. Anyone acquainted with the author's hands-on method of Riemann surfaces can be gratified through either the breadth and the intensity of the themes thought of the following. The exposition can be super transparent and thorough. somebody no longer conversant in the author's strategy is in for a true deal with. — Mathematical ReviewsThis is a thick and leisurely publication as a way to pay off repeated learn with many friendly hours – either for the newbie and the specialist. it's thankfully kind of self-contained, which makes it effortless to learn, and it leads one from crucial arithmetic to the “state of the artwork” within the idea of the Laplace–Beltrami operator on compact Riemann surfaces. even though it isn't encyclopedic, it's so wealthy in info and concepts … the reader could be thankful for what has been incorporated during this very pleasing publication. —Bulletin of the AMS The publication is especially good written and fairly available; there's a superb bibliography on the finish. —Zentralblatt MATH
By Gilles Pisier
Now in paperback, this renowned publication supplies a self-contained presentation of a few contemporary effects, which relate the quantity of convex our bodies in n-dimensional Euclidean house and the geometry of the corresponding finite-dimensional normed areas. The equipment hire classical principles from the idea of convex units, chance conception, approximation idea, and the neighborhood idea of Banach areas. the 1st a part of the e-book provides self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality. within the moment half Pisier provides a close exposition of the lately brought periods of Banach areas of susceptible cotype 2 or vulnerable kind 2, and the intersection of the periods (weak Hilbert space). this article will be an outstanding selection for classes in research and chance idea.
By Kalyan B. Sinha, Debashish Goswami
The classical idea of stochastic approaches has vital purposes coming up from the necessity to describe irreversible evolutions in classical mechanics; analogously quantum stochastic procedures can be utilized to version the dynamics of irreversible quantum platforms. Noncommutative, i.e. quantum, geometry offers a framework during which quantum stochastic constructions will be explored. This booklet is the 1st to explain how those mathematical buildings are related.In specific, key rules of semigroups and entire positivity are mixed to yield quantum dynamical semigroups (QDS). Sinha and Goswami additionally advance a basic thought of Evans-Hudson dilation for either bounded and unbounded coefficients. the original gains of the ebook, together with the interplay of QDS and quantum stochastic calculus with noncommutative geometry and an intensive dialogue of this calculus with unbounded coefficients, will make it of curiosity to graduate scholars and researchers in sensible research, likelihood and mathematical physics.