Volume 115, Issue 4
November 2005, pages 371-526
pp 371-381 November 2005
On the series ∑_{k=1}^{∞} (_{k}^{3k})^{−1}k^{−n}x^{k}
In this paper we investigate the series ∑_{k=1}^{∞} (_{k}^{3k})^{−1}k^{−n}x^{k}. Obtaining some integral representations of them, we evaluated the sum of them explicitly forn = 0, 1, 2.
pp 383-389 November 2005
An algebra of absolutely continuous functions and its multipliers
The aim of this paper is to study the algebraAC_{p} of absolutely continuous functionsf on [0,1] satisfying f(0) = 0,f ’ ∈ L^{p}[0, 1] and the multipliers ofAC_{p}.
pp 391-397 November 2005
There are infinitely many limit points of the fractional parts of powers
Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα^{n}, n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational non-integer number, this result was proved by Vijayaraghavan.
pp 399-410 November 2005
Commutators of integral operators with variable kernels on Hardy spaces
LetT_{Ω,α} (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, T_{Ω,α}] be the commutator generated by T_{Ω,α} and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, T_{Ω,α}] on the Hardy spaces, under some assumptions such as theL^{r}-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators$$T_{\tilde \Omega ,\alpha } (0 \leqslant \alpha< n)$$. The smoothness conditions imposed on$$\tilde \Omega $$ are weaker than the corresponding known results.
pp 411-427 November 2005
On the orders of finite semisimple groups
The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning of such order coincidences through the transitive actions of compact Lie groups.
It is a theorem of Artin and Tits that a finite simple group is determined by its order, with the exception of the groups (A_{3}(2), A_{2}(4)) and(B_{n}(q), C_{n}(q)) forn ≥ 3,q odd. We investigate the situation for finite semisimple groups of Lie type. It turns out that the order of the finite group H($$\mathbb{F}_{_q } $$) for a split semisimple algebraic groupH defined over$$\mathbb{F}_{_q } $$, does not determine the groupH up to isomorphism, but it determines the field$$\mathbb{F}_{_q } $$ under some mild conditions. We then put a group structure on the pairs(H_{1},H_{2}) of split semisimple groups defined over a fixed field$$\mathbb{F}_{_q } $$ such that the orders of the finite groups H_{1}($$\mathbb{F}_{_q } $$) and H_{2}($$\mathbb{F}_{_q } $$) are the same and the groupsH_{i} have no common simple direct factors. We obtain an explicit set of generators for this abelian, torsion-free group. We finally show that the order coincidences for some of these generators can be understood by the inclusions of transitive actions of compact Lie groups.
pp 429-435 November 2005
Transversals in non-discrete groups
The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroupS with a Tychonoff topologyT, it is proved that there exists a Hausdorff topological group in whichS can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological right transversal(S, T_{S},T^{S}, o) is such thatT_{S} =T^{S} is a locally compact Hausdorff topology onS, thenS can be embedded as a right transversal of a closed subgroup in a Hausdorff topological group which is universal in some sense.
pp 437-444 November 2005
A note on generalized characters
For a compactly generated LCA group G, it is shown that the setH(G) of all generalized characters on G equipped with the compact-open topology is a LCA group andH(G) = Ĝ (the dual group ofG) if and only ifG is compact. Both results fail for arbitrary LCA groups. Further, ifG is second countable, then the Gel’fand space of the commutative convolution algebraC_{c}(G) equipped with the inductive limit topology is topologically homeomorphic toH(G).
pp 445-451 November 2005
Vector bundles with a fixed determinant on an irreducible nodal curve
LetM be the moduli space of generalized parabolic bundles (GPBs) of rankr and degree dona smooth curveX. LetM_{−L} be the closure of its subset consisting of GPBs with fixed determinant− L. We define a moduli functor for whichM_{−L} is the coarse moduli scheme. Using the correspondence between GPBs onX and torsion-free sheaves on a nodal curveY of whichX is a desingularization, we show thatM_{−L} can be regarded as the compactified moduli scheme of vector bundles onY with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves onY. The relation to Seshadri-Nagaraj conjecture is studied.
pp 453-459 November 2005
Topologically left invariant means on semigroup algebras
LetM(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroupS with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions forM(S)* to have a topologically left invariant mean.
pp 461-476 November 2005
Basic topological and geometric properties of Cesàro-Orlicz spaces
Yunan Cui Henryk Hudzik Narin Petrot Suthep Suantai Alicja Szymaszkiewicz
Necessary and sufficient conditions under which the Cesàro-Orlicz sequence spaceces_{ϕ} is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spacesces_{ϕ} have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements inces_{ϕ} can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spacesces_{ϕ} are given.
pp 477-482 November 2005
On topological properties of the Hartman-Mycielski functor
We investigate some topological properties of a normal functorH introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM. We prove that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactumX and each denseσ-compact subsetY.
pp 483-492 November 2005
D-boundedness andD-compactness in finite dimensional probabilistic normed spaces
In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion ofD-compactness and D-boundedness in probabilistic normed spaces.
pp 493-498 November 2005
A functional central limit theorem for a class of urn models
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems are available in the two color case.
pp 499-508 November 2005
A-Statistical extension of the Korovkin type approximation theorem
In this paper, using the concept ofA-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a functionf by means of a sequenceL_{n}f of positive linear operators.
pp 509-517 November 2005
Large time behaviour of solutions of a system of generalized Burgers equation
In this paper we study the asymptotic behaviour of solutions of a system ofN partial differential equations. WhenN = 1 the equation reduces to the Burgers equation and was studied by Hopf. We consider both the inviscid and viscous case and show a new feature in the asymptotic behaviour.
pp 519-523 November 2005 Subject Index
pp 524-526 November 2005 Author Index
Current Issue
Volume 129 | Issue 5
November 2019
Click here for Editorial Note on CAP Mode
© 2017-2019 Indian Academy of Sciences, Bengaluru.