• Volume 105, Issue 3

August 1995,   pages  259-369

• Lifting orthogonal representations to spin groups and local root numbers

Representations ofDk*k* for a quaternion division algebraDk over a local fieldk are orthogonal representations. In this note we investigate when these orthogonal representations can be lifted to the corresponding spin group. The results are expressed in terms of local root number of the representation.

• Irrationality of linear combinations of eigenvectors

A givenn ×n matrix of rational numbers acts onCπ and onQπ. We assume that its characteristic polynomial is irreducible and compare a basis of eigenvectors forCπ with the standard basis forQπ. Subject to a hypothesis on the Galois group we prove that vectors from these two bases are as independent of each other as possible.

• On the zeros ofζ(1)(s)a (on the zeros of a class of a generalized Dirichlet series — XVII)

Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forllo =lo(a) (lo being a large constant). In particular for the precise results on the zeros ofζ(1)(s)a (a any complex constant andllo) see Theorems 1 and 2 of the introduction.

• A note on the growth of topological Sidon sets

We give an estimate for the number of elements in the intersection of topological Sidon sets inRn with compact convex subsets and deduce a necessary and sufficient conditions for an orbit of a linear transformation ofRn to be a topological Sidon set.

• Characterization of polynomials and divided difference

For distinct points x1,x2,…,xn in ℛ (the reals), letϕ[x1, x2,…,xn] denote the divided difference ofϕ. In this paper, we determine the general solutionϕ,g: ℛ → ℛ of the functional equationϕ[x1,x2,…,xn] =g(x1,+ x2 + … + xn) for distinct x1,x2,…, xn in ℛ without any regularity assumptions on the unknown functions.

• A theorem concerning a product of a general class of polynomials and theH-function of several complex variables

A theorem concerning a product of a general class of polynomials and theH-function of several complex variables is given. Using this theorem certain integrals and expansion formula have been obtained. This general theorem is capable of giving a number of new, interesting and useful integrals, expansion formulae as its special cases.

• Certain bilateral generating relations for generalized hypergeometric functions

Recently, we introduced a class of generalized hypergeometric functionsIn:(bq)/α:(ap) (x, w) by using a difference operator Δx,w, where$$\Delta _{x,w} f(x)\frac{{f(x + w) - f(x)}}{w}$$. In this paper an attempt has been made to obtain some bilateral generating relations associated withInga(x, w). Each result is followed by its applications to the classical orthogonal polynomials.

• A localization theorem for Laguerre expansions

Regularity properties of Laguerre means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localization theorem for Laguerre expansions.

• Degree of approximation of functions in the Hölder metric by (e, c) means

Degree of approximation of functions by the (e, c) means of its Fourier series in the Hölder metric is studied.

• The algebraAp((0, ∞)) and its multipliers

LetI =xεR: 0≤x≤∞ be the locally compact semigroup with addition as binary operation and the usual interval topology. The purpose of this note is to study the algebraAp(I) of elements inL1(I) whose Gelfand transforms belong toLp(Î), whereÎ denotes maximal ideal space ofL1(I). The multipliers ofAp(I) have also been identified.

• Reflection of P-waves in a prestressed dissipative layered crust

The paper deals with overall reflection and transmission response of seismic P-waves in a multilayered medium where the whole medium is assumed to be dissipative and under uniform compressive initial stress. The layers are assumed to be homogeneous, each having different material properties. Using Biot’s theory of incremental deformation, analytical solutions are obtained by matrix method. Numerical results for a stack of four layers — modelling earth’s upper layers, show a decreasing trend in both the Reflection CoefficientsRDPP andRDPS of the reflected P and S-waves.

• Computer extended series solution to viscous flow between rotating discs

The problem of injection (suction) of a viscous incompressible fluid through a rotating porous disc onto a rotating co-axial disc is studied using computer extended series. The universal coefficients in the low Reynolds number perturbation expansion are generated by delegating the routine complex algebra to computer. Various cases leading to specific types of flows are studied. Analytic continuation of the series solution yields results which agree favourably with pure numerical findings up to moderately large Reynolds number. The precise variation of lift as a function of R is established in each case.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019