{"product_id":"pick-interpolation-and-hilbert-function-spaces-paperback-softback-9781470468552","title":"Pick Interpolation and Hilbert Function Spaces (Paperback \/ softback) 9781470468552","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePick Interpolation and Hilbert Function Spaces\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eJim Agler (Author), John E. McCarthy (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470468552\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 1 January 2002\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e308 pages\u003cbr\u003e25.7 x 18.3 x 2.3 cm, 0.608 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eWritten in a clear, straightforward style, at a level to make it accessible to someone—a mid-level graduate student, say—who wishes to study the material in detail for the first time ... contains exercises ... as well as ... open questions. It brings the reader up to the current 'state of the art' and so will be a valuable resource for the specialist ... would be an excellent basis for a graduate seminar or topics course.\"\" — \u003cem\u003eMathematical Reviews\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\"\"Material is wonderfully presented, and the book serves as a lovely introduction to the subject. It is written by two authorities in the field, and helps grad students get entry into an exciting, modern, and very active research area.\"\" — Palle Jorgensen\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^\\infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^\\infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces.\u003cbr\u003e\u003cbr\u003eThe authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003ePrerequisites and notation\u003c\/li\u003e\n\u003cli\u003e Introduction\u003c\/li\u003e\n\u003cli\u003e Kernels and function spaces\u003c\/li\u003e\n\u003cli\u003e Hardy spaces\u003c\/li\u003e\n\u003cli\u003e $P^2(\\mu)$\u003c\/li\u003e\n\u003cli\u003e Pick redux\u003c\/li\u003e\n\u003cli\u003e Qualitative properties of the solution of the Pick problem in $H^\\infty(\\mathbb{D})$\u003c\/li\u003e\n\u003cli\u003e Characterizing kernels with the complete Pick property\u003c\/li\u003e\n\u003cli\u003e The universal Pick kernel\u003c\/li\u003e\n\u003cli\u003e Interpolating sequences\u003c\/li\u003e\n\u003cli\u003e Model theory I: Isometries\u003c\/li\u003e\n\u003cli\u003e The bidisk\u003c\/li\u003e\n\u003cli\u003e The extremal three point problem on $\\mathbb{D}^2$\u003c\/li\u003e\n\u003cli\u003e Collections of kernels\u003c\/li\u003e\n\u003cli\u003e Model theory II: Function spaces\u003c\/li\u003e\n\u003cli\u003e Localization\u003c\/li\u003e\n\u003cli\u003e Schur products\u003c\/li\u003e\n\u003cli\u003e Parrott's lemma\u003c\/li\u003e\n\u003cli\u003e Riesz interpolation\u003c\/li\u003e\n\u003cli\u003e The spectral theorem for normal $m$-tuples\u003c\/li\u003e\n\u003cli\u003e Bibliography\u003c\/li\u003e\n\u003cli\u003e Index\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52589078446360,"sku":"9781470468552","price":63.69,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/pick-interpolation-and-hilbert-function-spaces-paperback-softback-9781470468552","provider":"Freshly Printed Books","version":"1.0","type":"link"}