Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

X iv :0 90 5. 25 57 v2 [ m at h. R T ] 1 0 Ju n 20 09 JACOBI–TRUDY FORMULA FOR GENERALISED SCHUR POLYNOMIALS A.N. SERGEEV AND A.P. VESELOV Abstract. Jacobi–Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised Schur polynomials.

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2 × 2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and its relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on the m...

Abstract In the theory of orthogonal polynomials, as well in its intersection with harmonic analysis, it is an important problem to decide whether a given polynomial sequence $$(P_n(x))_{n\in \mathbb {N}_0}$$ ( P n x ) <...

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...

For all hyperbolic polynomials we proved in [11] a Lipschitz estimate of Jacobi matrices built by orthogonalizing polynomials with respect to measures in the orbit of classical Perron-Frobenius-Ruelle operators associated to hyperbolic polynomial dynamics (with real Julia set). Here we prove that for all sufficiently hyperbolic polynomials this estimate becomes exponentially better when the dim...