Orthogonal polynomials of several variables / (Record no. 517851)
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| 000 -LEADER | |
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| fixed length control field | 05678nam a22003858i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9781107786134 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160233.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 131216s2014||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781107786134 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9781107071896 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA404.5 |
| Item number | .D86 2014 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.55 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Dunkl, Charles F., |
| Dates associated with a name | 1941- |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Orthogonal polynomials of several variables / |
| Statement of responsibility, etc | Charles F. Dunkl, University of Virginia, Yuan Xu, University of Oregon. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | Second edition. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xvii, 420 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | volume 155 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Background -- The gamma and beta functions -- Hypergeometric series -- Orthogonal polynomials of one variable -- Classical orthogonal polynomials -- Modified classical polynomials -- Notes -- 2. Orthogonal polynomials in two variables -- Introduction -- Product orthogonal polynomials -- Orthogonal polynomials on the unit disk -- Orthogonal polynomials on the triangle -- Orthogonal polynomials and differential equations -- Generating orthogonal polynomials of two variables -- First family of koornwinder polynomials -- A related family of orthogonal polynomials -- Second family of koornwinder polynomials -- 3. General properties of orthogonal polynomials in several variables -- Notation and preliminaries -- Moment funtionals and orthogonal polynomials -- The three-term relation -- Jacobi matrices and commuting operators -- Further properties of the three-term relation -- Reproducing kernels and fourier orthogonal series -- Common zeros of orthogonal polynomials in several variables -- Gaussian cubature formulae -- Notes -- 4. Orthogonal polynomials on the unit sphere -- Spherical harmonics -- Orthoginal structures on Sd and on Bd -- Orthogonal structures on Bd and on Sd+m-1 -- Orthogonal structure on the simplex -- Van der corput -- Schaake inequality -- 5. Examples of orthogonal polynomials in several variables -- Orthogonal polynomials for simple weight functions -- Classical orthogonal polynomials on the unit ball -- Classical orthogonal polynomials on the simplex -- Orthogonal polynomials via symmetric functions -- Chebyshev polynomials to Type Ad -- Sobolev orthogonal polynomials on the unit ball -- 6. Root systems and coxeter groups -- Introduction and overview -- Root systems -- Invariant polynomials -- Differential-difference operators -- The intertwining operator -- The K-analogue of the exponential -- Invariant differential operators -- 7. Spherical harmonics associated with reflection groups -- h-Harmonic polynomials -- Inner products on polynomials -- Reproducing kernels and the poisson kernel -- Integration of the intertwining operator -- Example: Abelian group Z d/2 -- Example: Dihedral groups -- The dunk1 transform -- 8. Generalized classical orthogonal polynomials -- Generalized classical orthogonal polynomials on the ball -- Generalized classical orthogonal polynomials on the simplex -- Generalized hermite polynomials -- Generalized laguerre polynomials -- 9. Summability of orthogonal expansions -- General results on orthogonal expansions -- Orthogonal expansion on the sphere -- Orthogonal expansion on the ball -- Orthogonal expansion on the simplex -- Orthogonal expansion of Laguerre and Hermite polynomials -- Multiple Jacobi expansion -- 10. Orthogonal polynomials associated with symmetric groups -- Partitions, compositions and orderings -- Commuting self-adjoint operators -- The dual polynomials basis -- Sd-invariant subspaces -- Degree-changing recurrences -- Norm formulae -- Symmetric functions and jack polynomials -- Miscellaneous topics -- 11. Orthogonal polynomials associated with octahedral groups, and applications -- Operators of Type B -- Polynomial eigenfunctions of Type B -- Generalized binomial coefficients -- Hermite polynomials of Type B -- Calogero-Sutherland systems. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Orthogonal polynomials. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of several real variables. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Xu, Yuan, |
| Dates associated with a name | 1957- |
| Relator term | author. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9781107071896 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Encyclopedia of mathematics and its applications ; |
| Volume number/sequential designation | v. 155. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9781107786134">https://doi.org/10.1017/CBO9781107786134</a> |
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