{"title":"Mathematics: Abstract Analysis","description":"","products":[{"product_id":"generators-of-markov-chains","title":"Generators of Markov Chains","description":"Elementary treatments of Markov chains, especially those devoted to discrete-time and finite state-space theory, leave the impression that everything is smooth and easy to understand. This exposition of the works of Kolmogorov, Feller, Chung, Kato, and other mathematical luminaries, which focuses on time-continuous chains but is not so far from being elementary itself, reminds us again that the impression is false: an infinite, but denumerable, state-space is where the fun begins. If you have not heard of Blackwell's example (in which all states are instantaneous), do not understand what the minimal process is, or do not know what happens after explosion, dive right in. But beware lest you are enchanted: 'There are more spells than your commonplace magicians ever dreamed of.'","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43240141750511,"sku":"9781108495790","price":47.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108495790i.jpg?v=1661610180"},{"product_id":"encyclopedia-of-special-functions-the-askey-bateman-project","title":"Encyclopedia of Special Functions: The Askey-Bateman Project","description":"This is the first of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 1 contains most of the material on orthogonal polynomials, from the classical orthogonal polynomials of Hermite, Laguerre and Jacobi to the Askey-Wilson polynomials, which are the most general basic hypergeometric orthogonal polynomials. Separate chapters cover orthogonal polynomials on the unit circle, zeros of orthogonal polynomials and matrix orthogonal polynomials, with detailed results about matrix-valued Jacobi polynomials. A chapter on moment problems provides many examples of indeterminate moment problems. A thorough bibliography rounds off what will be an essential reference.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43940125114607,"sku":"9780521197427","price":63.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9780521197427i.jpg?v=1684323505"},{"product_id":"category-and-measure","title":"Category and Measure","description":"\u003cp\u003e\u003cspan\u003eTopological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a 'continuity structure', one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject's current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.\u003c\/span\u003e\u003c\/p\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":55035185529218,"sku":"9780521196079","price":110.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9780521196079i.jpg?v=1741879302"}],"url":"https:\/\/www.cambridgebookshop.co.uk\/collections\/mathematics-abstract-analysis.oembed","provider":"Cambridge University Press Bookshop","version":"1.0","type":"link"}