Showing papers on "Biorthogonal system published in 1990"

Explicit orthonormal Clebsch-Gordan coefficients of SU(3)

Abstract: The construction of the explicit algebraic‐polynomial expressions for the nonmultiplicity‐free orthonormal Clebsch–Gordan (Wigner) coefficients of SU(3)⊇U(2) is completed in the case of the paracanonical coupling scheme related with the explicit minimal biorthogonal systems by means of the Hecht or Gram–Schmidt process. The direct and inverse orthogonalization coefficients (the first of them being equivalent to the boundary orthonormal isofactors) are expressed, up to explicitly given multiplicative factors, in terms of the numerator and denominator polynomials related with the auxiliary Aλ function of Louck, Biedenharn, and Lohe that appears as a fragment of the denominator G‐functions of canonical SU(3) tensor operators.

Image restoration using biorthogonal wavelet transform

Abstract: A well-known method to solve ill-posed problem in image restoration is to use regularization techniques. The purpose of this paper is to propose a new scheme for digital image restoration based on a regularization method and on the BiOrthogonal Wavelet Transform. We show that, in cases where the blur function can be considered a scale function of a biorthogonal multiresolution analysis, it is possible to obtain an efficient family of regularization operators from the convolution operator alone.

Multivariable biorthogonal continuous–discrete Wilson and Racah polynomials

Abstract: Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables The latter are referred to as the multivariable biorthogonal Racah polynomials Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials

On a biorthogonal system associated with uniform asymptotic expansions

Abstract: In the present paper, a family of rational functions is introduced, and the two families form a biorthogonal system on a contour in the complex plane. The system can be viewed as a generalization of the families {z n } and {z −n−1 }, which occur in Taylor expansions and the Cauchy integrals of analytic functions. Explicit representations of the rational functions are given together with the rigorous estimates

Spectral analysis of biorthogonal expansions of functions, and exponential series

Abstract: The author studies the spectral properties of the operator A = id/dt in the space L2(0, 1), whose domain of definition is the kernel of some functional that is bounded in W21(0, 1) but not bounded in L2(0, 1). Necessary and sufficient conditions are given under which the operators ±iA generate C0-semigroups, and criteria for the similarity of A with a dissipative operator are proved. The results are used to study the basis properties of families of exponentials and to solve S. G. Krein's problem on the description of generators of semigroups in terms of their dissipative extensions. The solvability of integral equations of Delsarte type for mean periodic extensions of functions is also proved. Bibliography: 32 titles.