The family of general Jacobi polynomials P (α,β) n where α, β ∈ C can be characterised by complex (nonhermitian) orthogonality relations (cf. [15]). The special subclass of Jacobi polynomials P (α,β) n where α, β ∈ R are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the n real zeros, have been well studied. There is another spe...

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

We study the effect of wave function orthogonality in the rela-tivistic treatment of the nucleon removal reactions (γ, p) and (e, e ′ p). The continuum wave function describing the outgoing nucleon is made orthogonal to the relevant bound states using the Gram-Schmidt procedure. This procedure has the advantage of preserving the asymp-totic character of the continuum wave function and hence the...

Orthogonality of the Jacobi and of Laguerre polynomials, P (α,β) n and L (α) n , is established for α, β ∈ C \ Z−, α + β 6= −2,−3, . . . using the Hadamard finite part of the integral which gives their orthogonality in the classical cases. Riemann-Hilbert problems that these polynomials satisfy are found. The results are formally similar to the ones in the classical case (when Rα,Rβ > −1).

This paper proposes an inductive method to construct bases for spaces of spherical harmonics over the unit sphere Ω2q of Cq. The bases are shown to have many interesting properties, among them orthogonality with respect to the inner product of L(Ω2q). As a bypass, we study the inner product [f, g] = f(D)(g(z))(0) over the space P(Cq) of polynomials in the variables z, z ∈ Cq, in which f(D) is t...