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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 12
- .......... Page(s) .......... 501
- .......... Page(s) .......... 501
- We give a generalization of the theorem of Christol, Kamae, Mendès France and Rauzy [4]: a multisequence with k indices and with values in a finite field K with characteristic p is p-automatic if and only if the associated formal power series is algebraic over the field K(X1,...,X). This leads to an easy proof of a theorem of Deligne: if a formal double power series is algebraic over K(X, Y), then its diagonal is algebraic over K(X).
- .......... Page(s) .......... 505
- We prove that associated to a group extension
and a G-group H, there exists a 5-term exact sequence in non-abelian cohomology which measures the obstruction to the image of the map . This sequence reduces to the one obtained by Hochschild and Serre in the case of H being an abelian group.
- .......... Page(s) .......... 509
- .......... Page(s) .......... 509
- The problem is to classify quasi-crystallographic groups of icosahedral type with a group of translations of rank 6, up to conjugation within the affine group. We show how this question can be reduced to that of classifying crystallographic groups of this type in the 6-dimensional Euclidean space. We give a complete and explicit classification: there are three invariant lattices and two crystallographic groups which correspond to each of these lattices.
- .......... Page(s) .......... 513
- .......... Page(s) .......... 513
- On Hilbert spaces all operators of classes under consideration (restrictions of quasi-normal operators, quasi-isometric and quasi-unitary operators, convolution operators at least in commutative case) are semi-simple. This is no more true when the space is not a Hilbert space. For instance convolution operators on L1(G), G compact group, by summable functions, or translation operators on Lp(G), , G locally compact group, are not semi-simple, except trivial cases.
- .......... Page(s) .......... 517
- The maximum entropy principle gives a way to reconstruct spectral density from partial information (the trigonometric moment problem) we give sufficient conditions in the d-dimensional case, and a complete study in the case d=1.
- .......... Page(s) .......... 521
- We show the uniqueness and we give necessary and sufficient conditions for the existence of positive solutions of the equation where , denotes the p-Laplacian and is assumed to be decreasing.
- .......... Page(s) .......... 525
- We solve the ramified Cauchy problem with characteristics of constant multiplicity when the second member has a special form.
- .......... Page(s) .......... 529
- We prove that is a minimizing harmonic map from into for all .
- .......... Page(s) .......... 533
- .......... Page(s) .......... 533
- Some functional calculus for a bounded operator T in a Banach space are introduced and properties about the existence of invariant subspaces for T are deduced.
- .......... Page(s) .......... 537
- Bercovici has recently show in [2] that. Using his technique and those introduced in [10] we prove that (for a certain r). It follows that, for any T in , the weak-operator and weak* topologies coïncide on , the dual algebra generated by T, and that is weak-operator topology closed. We obtain also new criteria for membership in the classes (r) (in fact, by [9], in the classes and ) for example
- .......... Page(s) .......... 541
- .......... Page(s) .......... 541
- We use the relative Riemann-Roch theorem to prove the Castelnuovo-Severi inequality in a more general framework.
- Real algebraic morphisms with values in S and algebraic K-theory, Jacek BOCHNAK and Wojciech KUCHARZ.......... Page(s) .......... 545
- One studies the set of regular functions from a compact nonsingular real algebraic variety X of dimension n into the unit sphere Sn. One observes a difference of behavior between the case of even and odd dimension. The results are related to properties of the group of K-theory of the ring of regular functions from X into .
- .......... Page(s) .......... 553
- .......... Page(s) .......... 553
- Over a pseudo-riemannian manifold, we generalise a non traditional spinor concept by some torogonal extension; we obtain a complex line bundle: his curvature give the usual symplectic case to study the Kostant-Souriau prequantization.
- .......... Page(s) .......... 557
- .......... Page(s) .......... 557
- The Heegaard splittings of Seifert manifolds over S2 with 3 exceptional fibres are classified with respect to isotopies and homeomorphisms. In general there are 3 different homeomorphism classes. Moreover we determine exactly when a homeomorphism class is also an isotopy class.
- .......... Page(s) .......... 565
- .......... Page(s) .......... 565
- We study the minimization of the functional
- where u is a map from the unit ball into the unit sphere which stisfies on , and where , , are strictly positive constants. We show that does not minimize E if. We exhibit a map which minimizes E in the degenerate case .
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