1 edition of **Approximation Theory and Harmonic Analysis on Spheres and Balls** found in the catalog.

- 319 Want to read
- 26 Currently reading

Published
**2013**
by Springer New York, Imprint: Springer in New York, NY
.

Written in English

- Approximations and Expansions,
- Special Functions,
- Mathematics,
- Fourier analysis,
- Global analysis (Mathematics),
- Analysis

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography.This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

**Edition Notes**

Statement | by Feng Dai, Yuan Xu |

Series | Springer Monographs in Mathematics |

Contributions | Xu, Yuan, SpringerLink (Online service) |

Classifications | |
---|---|

LC Classifications | QA299.6-433 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | XVIII, 440 p. 1 illus. |

Number of Pages | 440 |

ID Numbers | |

Open Library | OL27017765M |

ISBN 10 | 9781461466604 |

These include approximation on compact sets (such as spheres, balls, or compact ho mogeneous manifolds), spherical designs and energy functionals, interpolation by radial basis functions and by splines, frame theory and Gabor analysis, re finable function systems and subdivision, properties of harmonic, polyharmonic and blending functions. Nonlinear approximation, hyperbolic PDEs, conservation laws, numerical quadrature on balls in R n. Bojan Popov Conservation laws, linear transport equations, approximation theory, numerical analysis of PDEs N. Sivakumar Splines, radial basis functions, approximation and interpolation on spheres, classical analysis, cardinal interpolation Joseph.

Books (with Charles F. Dunkl) "Orthogonal Polynomials of Several Variables", Second Edition, Encyclopedia of Mathematics and its Applications, vol. , Cambridge Univ. Press, ISBN: (with Feng Dai) "Approximation Theory and Harmonics Analysis on Spheres and Balls", Springer Monographs in Mathematics, Springer, ISBN: (Print) . This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer Monographs in Mathematics} by Springer in

In the book Approximation Theory and Harmonic Analysis on Spheres and Balls by Dai Feng and Xu Yuan, there is a Theorem: Theorem Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai; Yuan Xu and Publisher Springer. Save up to 80% by choosing the eTextbook option for ISBN: , The print version of this textbook is ISBN: ,

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This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this by: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area.5/5(1).

Download Citation | Approximation theory and harmonic analysis on spheres and balls | 1 Spherical Harmonics.- 2 Convolution and Spherical Harmonic Expansion.- 3 Littlewood-Paley Theory and.

Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics) eBook: Dai, Feng, Xu, Yuan: : Kindle Store5/5(1). This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this : Springer New York.

Approximation Theory and Harmonic Analysis on Spheres and Balls - springer springer, This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area.

This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer Monographs in Mathematics} by Springer in The two participants, Dai and Xu, have been working on a research monograph entitled “Approximation theory and Harmonic Analysis on Unit Sphere”, which will be the ﬁrst research monograph dedicated entirely to this subject.

One of the main objectives of the program is for the two authors to discuss the organization and details of the book. The boundary usually makes analysis on the domain more difficult. It turns out, however, that analysis on the unit ball is closely related to analysis on the unit sphere.

Indeed, a large portion of harmonic analysis on the unit ball can be deduced from its counterparts on the sphere. Download Citation | Harmonic Analysis on the Unit Ball | Unlike the unit sphere, the unit ball is a domain that has a boundary.

The boundary usually makes analysis on the domain more difficult. Analogues of the Funk–Hecke formula for spherical harmonics are proved for Dunkl's h‐harmonics associated to the reflection groups, and for orthogonal polynomials related to h‐harmonics on the unit b.

Get this from a library. Approximation theory and harmonic analysis on spheres and balls. [Feng Dai; Yuan Xu]. Abstract.

There have been continuing researches in approximation theory and harmonic analysis on the unit sphere throughout the last century. For approximation theory, one of the historical highlights is the complete characterization of best approximation by polynomials on the sphere in terms of a modulus of smoothness defined via the spherical means, the accumulation point of decades of works.

Dai, F. and Xu, Y., Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics), Springer (New York, NY, ). Dunkl, C. and Xu, Y., Orthogonal Polynomials of Several Variables, Cambridge University Press (Cambridge, ). funk–hecke formula for orthogonal polynomials on spheres and on balls - volume 32 issue 4 - yuan xu Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites.

This monograph covers approximation theory and harmonic analysis on balls and spheres. It provides mainstream material on the subject as well as more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes, and includes several applications, including cubature formulas, distribution of points on the sphere, and the.

Approximation Theory and Harmonic Analysis on Spheres and Balls, () Numerical integration with polynomial exactness over a spherical cap. Advances in. Agahanov, A method of constructing orthogonal polynomials of two variables for a certain class of weight functions, Vestnik 20 (), no.

19, 5–10 (Russian, with English summary).MR Feng Dai and Yuan Xu, Approximation theory and harmonic analysis on spheres and balls, Springer Monographs in Mathematics, Springer, New York, Orthogonal polynomials on the unit sphere in RRd+1 and on the unit ball in RRd are shown to be closely related to each other for symmetric weight functions.

Furthermore, it is shown that a large cl. Feng Dai and Yuan Xu, Approximation theory and harmonic analysis on spheres and balls, Springer Monographs in Mathematics, Springer, New York, MR [3].Approximation Theory and Harmonic Analysis on Spheres and Balls.

Series: Springer Monographs in MathematicsXVI, p. Hardcover Information ISBN Due: Ap About this book. Written by experts in the field Contains up-to-date research in approximation theory and harmonic analysis on balls and spheres.Project Euclid - mathematics and statistics online.

Strictly and non-strictly positive definite functions on spheres Gneiting, Tilmann, Bernoulli, ; Positive definiteness, reproducing kernel Hilbert spaces and beyond Ferreira, J.

C. and Menegatto, V.