Volume 109, Issue 3
August 1999, pages 231-332
pp 231-239 August 1999
Shreeram S Abhyankar Paul A Loomis
A general technique is developed to enlarge the Galois group of an equation from a subgroup of a finite classical isometry group towards the corresponding similitude group.
pp 241-256 August 1999
Remarks on the wonderful compactification of semisimple algebraic groups
We prove that ifG is a semisimple algebraic group of adjoint type over the field of complex numbers,H is the subgroup of all fixed points of an involution σ ofG that is induced by an involution σ of the simply connected coveringĜ ofG, then the wonderful compactification$$\overline {G/H} $$ of the homogeneous spaceG/H is isomorphic to the G.I.T quotientG^{ss}(L)//H of the wonderful compactificationG ofG for a suitable choice of a line bundleL onG. We also prove a functorial property of the wonderful compactifications of semisimple algebraic groups of adjoint type.
pp 257-270 August 1999
Seiberg-Witten invariants — An expository account
Kapil H Paranjape Vishwambhar Pati
The Seiberg-Witten monopole equations, and a new invariant for 4-manifolds which results from these equations, are introduced in this paper.
pp 271-298 August 1999
The theorem of Kronheimer-Mrowka
A proof of the conjecture of Thom (algebraic curves in the complex projective plane minimize genus within their homology class) due to Kronheimer-Mrowka is presented. The proof uses the mod-2 Seiberg-Witten invariants.
pp 299-302 August 1999
Infinitely divisible probabilities on linearp-adic groups
In this paper we extend the work of Shah, on the structure of infinitely divisible probabilities onp-adic linear groups, to give a classification for all such probabilities.
pp 303-307 August 1999
A short note on weighted mean matrices
In the present paper we have established a relation between (N, p_{n}) and (N, q_{n}) weighted mean matrices, when considered as bounded operators on 1^{p}, 1 < p < ∞.
pp 309-315 August 1999
L^{1} (μ, X) as a constrained subspace of its bidual
In this note we consider the property of being constrained in the bidual, for the space of Bochner integrable functions. For a Banach spaceX having the Radon-Nikodym property and constrained in its bidual and forY ⊂ X, under a natural assumption onY, we show thatL^{1} (μ, X/Y) is constrained in its bidual andL^{1} (μ, Y) is a proximinal subspace ofL^{1}(μ, X). As an application of these results, we show that, ifL^{1}(μ, X) admits generalized centers for finite sets and ifY ⊂ X is reflexive, thenL^{1}μ, X/Y) also admits generalized centers for finite sets.
pp 317-323 August 1999
A result on the composition of distributions
LetF be a distribution and letf be a locally summable function. The distributionF(f) is defined as the neutrix limit of the sequenceF_{n}(f), whereF_{n}(x) = F(x) * δ_{n}(x) andδ_{n}(x) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). The distribution (x^{r})^{−s} is valuated forr, s = 1,2, ….
pp 325-332 August 1999
Existence of solutions of neutral functional integrodifferential equation in Banach spaces
In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space. The results are obtained by using the Schaefer fixed-point theorem.
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