共查询到20条相似文献,搜索用时 15 毫秒
1.
Carlos Gamas 《Linear and Multilinear Algebra》2000,47(2):151-173
Let λ be an irreducible character of Sn corresponding to the partition (r,s) of n. Let A be a positive semidefinite Hermitian n × n matrix. Let dλ(A) and per(A) be the immanants corresponding to λ and to the trivial character of Sn, respectively. A proof of the inequality dλ(A)≤λ(id)per(A) is given. 相似文献
2.
We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics, which allows us, analogously to zonal harmonics, to construct Poisson kernels for polyharmonic functions on the union of rotated balls. We find the representation of Poisson kernels and zonal polyharmonics in terms of the Gegenbauer polynomials. We show the connection between the classical Poisson kernel for harmonic functions on the ball, Poisson kernels for polyharmonic functions on the union of rotated balls, and the Cauchy-Hua kernel for holomorphic functions on the Lie ball. 相似文献
3.
Spherical Bessel functions and explicit quadrature formula 总被引:1,自引:0,他引:1
An evaluation of the derivative of spherical Bessel functions of order at its zeros is obtained. Consequently, an explicit quadrature formula for entire functions of exponential type is given.
4.
Joseph A. Wolf 《Journal of Functional Analysis》2006,239(1):127-136
We study spherical functions on Euclidean spaces from the viewpoint of Riemannian symmetric spaces. Here the Euclidean space En=G/K where G is the semidirect product Rn⋅K of the translation group with a closed subgroup K of the orthogonal group O(n). We give exact parameterizations of the space of (G,K)—spherical functions by a certain affine algebraic variety, and of the positive definite ones by a real form of that variety. We give exact formulae for the spherical functions in the case where K is transitive on the unit sphere in En. 相似文献
5.
A new class of locally supported radial basis functions
on the (unit) sphere is introduced by forming an infinite number
of convolutions of "isotropic finite elements." The resulting up
functions show useful properties: They are locally supported and
are infinitely often differentiable. The main properties of these
kernels are studied in detail. In particular, the development of a
multiresolution analysis is given based on locally supported zonal
functions within the reference space of square-integrable
functions over the sphere. 相似文献
6.
Multi-vector Spherical Monogenics, Spherical Means and Distributions in Clifford Analysis 总被引:2,自引:0,他引:2
Rred BRACKX Bram De KNOCK Hennie De SCHEPPER 《数学学报(英文版)》2005,21(5):1197-1208
New higher-dimensional distributions have been introduced in the framework of Clifford analysis in previous papers by Brackx, Delanghe and Sommen. Those distributions were defined using spherical co-ordinates, the "finite part" distribution Fp x+^μ on the real line and the generalized spherical means involving vector-valued spherical monogenics. In this paper, we make a second generalization, leading to new families of distributions, based on the generalized spherical means involving a multivector-valued spherical monogenic. At the same time, as a result of our attempt at keeping the paper self-contained, it offers an overview of the results found so far. 相似文献
7.
N. Ressayre 《Advances in Mathematics》2010,224(5):1784-1800
Let G be a connected reductive algebraic group over an algebraically closed field K of characteristic zero. Let G/B denote the complete flag variety of G. A G-homogeneous space G/H is said to be spherical if H has finitely many orbits in G/B. A class of spherical homogeneous spaces containing the tori, the complete homogeneous spaces and the group G (viewed as a G×G-homogeneous space) has particularly nice properties. Namely, the pair (G,H) is called a spherical pair of minimal rank if there exists x in G/B such that the orbit H.x of x by H is open in G/B and the stabilizer Hx of x in H contains a maximal torus of H. In this article, we study and classify the spherical pairs of minimal rank. 相似文献
8.
B. J. C. Baxter 《Foundations of Computational Mathematics》2008,8(3):395-407
A radial basis function (RBF) has the general form
where the coefficients a
1,…,a
n
are real numbers, the points, or centres, b
1,…,b
n
lie in ℝ
d
, and φ:ℝ
d
→ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance
(Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline
spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported
when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy
certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities,
with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions.
Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore,
we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite
functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we
are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore,
the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric
integration.
Dedicated to Arieh Iserles on the occasion of his 60th birthday. 相似文献
9.
Ke Ye 《Linear algebra and its applications》2011,435(5):1085-1098
Immanants are homogeneous polynomials of degree n in n2 variables associated to the irreducible representations of the symmetric group Sn of n elements. We describe immanants as trivial Sn modules and show that any homogeneous polynomial of degree n on the space of n×n matrices preserved up to scalar by left and right action by diagonal matrices and conjugation by permutation matrices is a linear combination of immanants. Building on works of Duffner [5] and Purificação [3], we prove that for n?6 the identity component of the stabilizer of any immanant (except determinant, permanent, and π=(4,1,1,1)) is Δ(Sn)?T(GLn×GLn)?Z2, where T(GLn×GLn) is the group consisting of pairs of n×n diagonal matrices with the product of determinants 1, acting by left and right matrix multiplication, Δ(Sn) is the diagonal of Sn×Sn, acting by conjugation (Sn is the group of symmetric group) and Z2 acts by sending a matrix to its transpose. Based on the work of Purificação and Duffner [4], we also prove that for n?5 the stabilizer of the immanant of any non-symmetric partition (except determinant and permanent) is Δ(Sn)?T(GLn×GLn)?Z2. 相似文献
10.
11.
In this paper we analyse a hybrid approximation of functions on the sphere by radial basis functions combined with polynomials, with the radial basis functions assumed to be generated by a (strictly)
positive definite kernel. The approximation is determined by interpolation at scattered data points, supplemented by side
conditions on the coefficients to ensure a square linear system. The analysis is first carried out in the native space associated
with the kernel (with no explicit polynomial component, and no side conditions). A more refined error estimate is obtained
for functions in a still smaller space. Numerical calculations support the utility of this hybrid approximation.
相似文献
12.
We review in these notes the theory of equivariant embeddings of spherical homogeneous spaces. Given a spherical homogeneous space G/H, the normal equivariant embeddings of G/H are classified by combinatorial objects called colored fans, which generalize the fans appearing in the classification of toric varieties and which encode several geometric properties of the corresponding variety. 相似文献
13.
Yoshihiro Mizuta 《复变函数与椭圆型方程》2019,64(2):283-299
We introduce central generalized Orlicz–Morrey spaces on the unit ball, and study the weighted behavior of spherical means for Riesz potentials of functions in those spaces. We also treat Orlicz–Morrey–Sobolev functions which are monotone in the punctured unit ball in the sense of Lebesgue. 相似文献
14.
A formula of a radial derivative
is obtained with the aid of derivatives with respect to and to of the functions closely connected with the spherical Poisson integral
and the boundary values are determined for
. The boundary values are also found for partial derivatives with respect to the Cartesian coordinates
. 相似文献
15.
Willi Freeden 《Journal of Computational and Applied Mathematics》1984,11(3):367-375
The purpose of the paper is to adapt to the spherical case the basic theory and the computational method known from surface spline interpolation in Euclidean spaces. Spline functions are defined on the sphere. The solution process is made simple and efficient for numerical computation. In addition, the convergence of the solution obtained by spherical spline interpolation is developed using estimates for Legendre polynomials. 相似文献
16.
The main purpose of the present paper is to employ spherical basis functions (SBFs) to study uniform distribution of points on spheres. We extend Weyl's criterion for uniform distribution of points on spheres to include a characterization in terms of an SBF. We show that every set of minimal energy points associated with an SBF is uniformly distributed on the spheres. We give an error estimate for numerical integration based on the minimal energy points. We also estimate the separation of the minimal energy points. 相似文献
17.
18.
Da-Qian Lu 《Applied mathematics and computation》2012,218(9):5090-5098
General classes of Tricomi and Hermite-Tricomi functions are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials, and we mainly consider the properties of the general classes of 3-variable 2-index Tricomi functions and 2-index 4-variable 1-parameter Hermite-Tricomi functions. 相似文献
19.
R. Mehrem 《Applied mathematics and computation》2011,217(12):5360-5365
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identities for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions. 相似文献
20.
Béla Bajnok 《Designs, Codes and Cryptography》2000,21(1-3):11-18
We extend the concepts of sum-freesets and Sidon-sets of combinatorial number theory with the aimto provide explicit constructions for spherical designs. We calla subset S of the (additive) abelian group G
t-free if for all non-negative integers kand l with k+l t, the sum of k(not necessarily distinct) elements of S does notequal the sum of l (not necessarily distinct) elementsof S unless k=l and the two sums containthe same terms. Here we shall give asymptotic bounds for thesize of a largest t-free set in Z
n,and for t 3 discuss how t-freesets in Z
n can be used to constructspherical t-designs. 相似文献