Pick Interpolation And Hilbert Function Spaces Download Free (EPUB, PDF)
The 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. The 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.
Series: Graduate Studies in Mathematics (Book 44)
Hardcover: 328 pages
Publisher: American Mathematical Society; F First Edition edition (March 1, 2002)
Language: English
ISBN-10: 0821828983
ISBN-13: 978-0821828984
Product Dimensions: 1 x 7.2 x 10 inches
Shipping Weight: 1.7 pounds
Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
Best Sellers Rank: #2,926,448 in Books (See Top 100 in Books) #94 in Books > Science & Math > Mathematics > Transformations #23724 in Books > Textbooks > Science & Mathematics > Mathematics
Classical and modern.The "interpolation" part of the title refers to a classical result of G. Pick [1916], and R. Nevanlinna [1919]. They did it independently. Since the disk D (in one complex variable)is a model of a hyperbolic metric space, interpolation can't be done by just drawing straight lines. If two finite sets of points in D are given(same number of points in the two sets), the issue is to find an analytic function mapping D into itself, which at the same time matches up the points in one set with those in the other. The necessary and sufficient condition for the existence, and the solution, when it exists, is the classical issue. Since this, the framework has offered a wonderful testing ground for main trends in modern analysis, such as the theory of operators in Hilbert space, and for modern techniques in systems theory of engineering, and of scattering theory. The 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.
Pick Interpolation and Hilbert Function Spaces Picking | Picks | Locksmith | How To Lock Pick | How Can You Pick A Lock | How To Pick LOCKS! Pick A Lock in 5 seconds or Less Guaranteed! 250 Ultimate Funny Pick Up Lines: Hilarious, Cute, and Cheesy Pick Up Lines to Meet Women Is It Wrong to Try to Pick Up Girls in a Dungeon? Sword Oratoria, Vol. 1 - light novel (Is It Wrong to Try to Pick Up Girls in a Dungeon? On the Side: Sword Oratoria) Ruppel's Manual of Pulmonary Function Testing, 10e (Manual of Pulmonary Function Testing (Ruppel)) Manual of Pulmonary Function Testing, 9e (Manual of Pulmonary Function Testing (Ruppel)) Enterprise Risk Management - Straight to the Point: An Implementation Guide Function by Function (Viewpoints on ERM) Optimization in Function Spaces (Aurora: Dover Modern Math Originals) Introduction to Hilbert Space: And the Theory of Spectral Multiplicity (AMS Chelsea Publishing) Theory of Linear Operators in Hilbert Space (Dover Books on Mathematics) Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics) Man Candy: An Adult Coloring Book with 30 Hot Men and Pick-up Lines to Calm and Relax Muscles: Testing and Function, with Posture and Pain (Kendall, Muscles) Workbook and Lab Manual for Sonography: Introduction to Normal Structure and Function, 4e Workbook and Lab Manual for Sonography: Introduction to Normal Structure and Function, 3e Chinese Buddhist Monasteries: Their Plan and Its Function as a Setting for Buddhist Monastic Life Classic Human Anatomy: The Artist's Guide to Form, Function, and Movement Marks of Excellence: The Function and Variety of Trademarks Pick a Pickle: 50 Recipes for Pickles, Relishes, and Fermented Snacks Executive Function in the Classroom: Practical Strategies for Improving Performance and Enhancing Skills for All Students
