On the characteristic equation of Chebyshev matrices.
On the composition structure of the twisted Verma modules for
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra , including the explicit structure of singular vectors for both and one of its Lie subalgebras , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as -modules on the Schubert cells in the full flag manifold for .
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement...
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial...
On the convergence of the stochastic Galerkin method for random elliptic partial differential equations
In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity by random...
On the decay properties of the Franklin analyzing wavelet
On the derivatives of Bernstein polynomials: an application for the solution of high even-order differential equations.
On the distributional orthogonality of the general Pollaczek polynomials.
On the dual of a Commutative signed Hypergroup.
On the Dynamic Behaviour of Chebyshev Polynomials.
On the Galois group of generalized Laguerre polynomials
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed , Filaseta and Lam have shown that the th degree Generalized Laguerre Polynomial is irreducible for all large enough . We use our criterion to show that, under these conditions, the Galois group of is either the alternating or symmetric group on letters, generalizing results of Schur for .
On the inequality of P. Turán for Legendre polynomials.
On the irreducibility of the generalized Laguerre polynomials
On the Krall-type polynomials.
On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group
On the limit from -Racah polynomials to big -Jacobi polynomials.
On The Orthogonality Measure Of The ...-Pollaczek Polynomials.
On the polynomials orthogonal in the interval with the weight function
On the positivity of certain Cotes numbers.
On the q-Konhauser biorthogonal polynomials.