Skip to content
Register Sign in Wishlist

Orthogonal Polynomials of Several Variables

2nd Edition

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107071896

Hardback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.

    • Incorporates classical and modern approaches
    • Gives enough background information for readers to understand and apply symmetry techniques
    • Covers in detail the families of orthogonal polynomials for important weight functions
    Read more

    Reviews & endorsements

    Review of the first edition: 'This book is the first modern treatment of orthogonal polynomials of several real variables. It presents not only a general theory, but also detailed results of recent research on generalizations of various classical cases.' Mathematical Reviews

    Review of the first edition: 'This book is very impressive and shows the richness of the theory.' Vilmos Totik, Acta Scientiarum Mathematicarum

    'This is a valuable book for anyone with an interest in special functions of several variables.' Marcel de Jeu, American Mathematical Society

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Edition: 2nd Edition
    • Date Published: August 2014
    • format: Hardback
    • isbn: 9781107071896
    • length: 426 pages
    • dimensions: 240 x 159 x 28 mm
    • weight: 0.81kg
    • contains: 3 b/w illus.
    • availability: Available
  • Table of Contents

    Preface to the second edition
    Preface to the first edition
    1. Background
    2. Orthogonal polynomials in two variables
    3. General properties of orthogonal polynomials in several variables
    4. Orthogonal polynomials on the unit sphere
    5. Examples of orthogonal polynomials in several variables
    6. Root systems and Coxeter groups
    7. Spherical harmonics associated with reflection groups
    8. Generalized classical orthogonal polynomials
    9. Summability of orthogonal expansions
    10. Orthogonal polynomials associated with symmetric groups
    11. Orthogonal polynomials associated with octahedral groups and applications
    References
    Author index
    Symbol index
    Subject index.

  • Authors

    Charles F. Dunkl, University of Virginia
    Charles F. Dunkl is Professor Emeritus of Mathematics at the University of Virginia. Among his work one finds the seminal papers containing the construction of differential-difference operators associated to finite reflection groups and related integral transforms. Aspects of the theory are now called Dunkl operators, the Dunkl transform, and the Dunkl kernel. Dunkl is a Fellow of the Institute of Physics, and a member of SIAM and of its Activity Group on Orthogonal Polynomials and Special Functions, which he founded in 1990 and then chaired from 1990 to 1998.

    Yuan Xu, University of Oregon
    Yuan Xu is Professor of Mathematics at the University of Oregon. His work covers topics in approximation theory, harmonic analysis, numerical analysis, orthogonal polynomials and special functions, and he works mostly in problems of several variables. Xu is currently on the editorial board of five international journals and has been a plenary or invited speaker in numerous international conferences. He was awarded a Humboldt research fellowship in 1992–93 and received a Faculty Excellence Award at the University of Oregon in 2009. He is a member of SIAM and of its Activity Group on Orthogonal Polynomials and Special Functions.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×