Orthogonal Polynomials of Several Variables

We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation.

[1]  Attila Máté,et al.  Szegö’s extremum problem on the unit circle , 1991 .

[2]  M. Kowalski,et al.  The Recursion Formulas for Orthogonal Polynomials in n Variables , 1982 .

[3]  Charles F. Dunkl,et al.  Differential-difference operators associated to reflection groups , 1989 .

[4]  Yuan Xu,et al.  On zeros of multivariate quasi-orthogonal polynomials and Gaussian cubature formulae , 1994 .

[5]  Yuan Xu,et al.  On two-dimensional definite orthogonal systems and a lower bound for the number of nodes of associated cubature formulae , 1995 .

[6]  R. Askey.  Orthogonal Polynomials and Special Functions , 1975 .

[7]  Jean-François Richard,et al.  Methods of Numerical Integration , 2000 .

[8]  M. Kowalski,et al.  Orthogonality and Recursion Formulas for Polynomials in n Variables , 1982 .

[9]  T. MacRobert.  Higher Transcendental Functions , 1955, Nature.

[10]  Ronald Cools,et al.  On cubature formulae of degree 4k+1 attaining Möller's lower bound for integrals with circular symmetry , 1992 .

[11]  Yuan Xu,et al.  Block Jacobi matrices and zeros of multivariate orthogonal polynomials , 1994 .

[12]  M. Gekhtman,et al.  On the orthogonal polynomials in several variables , 1994 .

[13]  Yuan Xu,et al.  Fejér means for multivariate Fourier series , 1996 .

[14]  T. Koornwinder.  Two-Variable Analogues of the Classical Orthogonal Polynomials , 1975 .

[15]  Yuan Xu,et al.  Multivariate Gaussian cubature formulae , 1995 .

[16]  P. K. Suetin.  Orthogonal Polynomials in Two Variables , 1999 .

[17]  M. Anshelevich,et al.  Introduction to orthogonal polynomials , 2003 .

[18]  Ronald Cools,et al.  A new lower bound for the number of nodes in cubature formulae of degree 4 n + 1 for some circularly symmetric integrals , 1993 .

[19]  T. N. L. Patterson,et al.  Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory , 1978 .

[20]  Yuan Xu,et al.  On multivariate orthogonal polynomials , 1993 .

[21]  Charles F. Dunkl,et al.  Integral Kernels with Reflection Group Invariance , 1991, Canadian Journal of Mathematics.

[22]  J. Dombrowski.  Orthogonal Polynomials and Functional Analysis , 1990 .

[23]  marshall Stone Harvey,et al.  Linear Transformations In Hilbert Space And Their Applications To Analysis , 1932 .

[24]  Yuan Xu,et al.  A characterization of positive quadrature formulae , 1994 .

[25]  Christian Berg,et al.  Rotation invariant moment problems , 1991 .

[26]  H. M. Möller,et al.  Kubaturformeln mit minimaler Knotenzahl , 1976 .

[27]  Yuan Xu,et al.  On bivariate Gaussian cubature formulae , 1994 .