The Witt ring of a Brauer–Severi variety

For a Brauer–Severi variety X over a field k of characteristic not two, every symmetric bilinear space over X up to Witt equivalence is defined over k. Received: 2 February 1998     

Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

Strong approximation ofGSBV functions by piecewise smooth functions

Let Ω be an open and bounded subset ofR ⁿ with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R ^m ) whose jump setS _vis essentially closed and polyhedral and which are of classW ^{k, ∞} (S _v,R ^m) for every integerk are strongly dense inGSBV ^p(Ω,R ^m ), in the sense that every functionu inGSBV ^p(Ω,R ^m ) is approximated inL ^p(Ω,R ^m ) by a sequence of functions {v _k{_j∈N with the described regularity such that the approximate gradients ∇v _jconverge inL ^p(Ω,R ^nm ) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS _{v j} converges to the (n−1)-dimensional measure ofS _u. The structure ofS _v can be further improved in casep≤2.

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Sunto Sia Ω un aperto limitato diR ⁿ con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R ^m ) con insieme di saltoS _v essenzialmente chiuso e poliedrale che sono di classeW ^{k, ∞} (S _v,R ^m ) per ogni interok sono fortemente dense inGSBV ^p(Ω,R ^m ), nel senso che ogni funzioneu∈GSBV ^p(Ω,R ^m ) è approssimata inL ^p(Ω,R ^m ) da una successione di funzioni {v _j}_j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v _jconvergono inL ^p(Ω,R ^nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS _{v j}converge alla misura (n−1)-dimensionale diS _u. La struttura diS _vpuó essere migliorata nel caso in cuip≤2.

     

Berezin transform on¶compact Hermitian symmetric spaces

Let X=G ^* be a compact Hermitian symmetric space. We study the Berezin transform on L ²(X) and calculate its spectrum under the decomposition of L ²(X) into the irreducible representations of G ^*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X. Received: 10 September 1996 / Revised version: 10 September 1997     

Vibrational spectrum of uridine obtained by means of nonresonant-background-free CARS spectroscopy

Received: 18 June 1996/Revised version: 3 January 1997     

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps. Received: 10 June 1996 / In revised form: 9 August 1996     

Bouquet and join theorems for disentanglements

The disentanglement of certain augmentations is shown to be the topological join of a disentanglement and a Milnor fibre. The kth disentanglement of a finite map is defined and for corank 1 maps from ℂ ⁿ to ℂ ^{n +1} it is shown that they are homotopically equivalent to a wedge of spheres. Applications to the Mond conjecture are given. Oblatum 24-VII-2000 & 5-VII-2001?Published online: 12 October 2001