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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 18
- .......... Page(s) .......... 761
- .......... Page(s) .......... 761
- Using Apery's method for acceleration of convergence, we give an irrationality measure of the Carlitz's zeta function for F2(T) at 1.
- .......... Page(s) .......... 765
- It is proved that the derivatives of the Bessel polynomials of arbitrary order as well as, under a not very restrictive condition, the generalized Bessel polynomials, have the "minimum of real roots" property. The applied method is more elementary than that has been used so far to prove the analogous result concerning the Bessel polynomials. And then we compare these roots.
- .......... Page(s) .......... 769
- .......... Page(s) .......... 769
- In the framework of the deformation program (* products) initiated in [3], a nilpotent Fourier transform was introduced ([5], [7]). This transformation is canonically defined on the space (G) of C rapidly decreasing functions on the group G to a space of C functions on a dense open subset of g. We prove here that this transformation is continuous.
- .......... Page(s) .......... 773
- .......... Page(s) .......... 773
- We prove several inverse mapping theorems for set-valued maps defined on a complete metric space. Results are applied to the study of controllability of infinite dimensional control systems.
- .......... Page(s) .......... 777
- The only "harmonic" functions on a polycyclic discrete group, or on a solvable connected Lie group are the constants.
- .......... Page(s) .......... 781
- .......... Page(s) .......... 781
- We study a Dirichlet problem of general type on a harmonic space in the sense of Brelot. We show that the solutions verify a kind of L1 convergence to the boundary data. We consider the Green lines in an open set of which admits a Green function. Finally we give a criterion for the "convergence of a family of lines" in the compactification of R. S. Martin.
- .......... Page(s) .......... 785
- .......... Page(s) .......... 785
- We present new results on existence, uniqueness and the maximal regularity on the abstract elliptic equation of the second order with non homogeneous boundary conditions and without density of domain, but with necessary hypothesis on compatibility of data and boundary conditions. We complete this study by presenting two tables summarising the principal hypothesis used until now to resolve this equation and the parabolic equation.
- .......... Page(s) .......... 793
- .......... Page(s) .......... 793
- We describe a homotopy-invariant algebraic K-theory KH for both associative rings and schemes. It agrees with Quillen K-theory K for regular rings and schemes, and if coefficients mod l are taken and l is a unit. The Fundamental Theorem of K-theory holds for KH. KH-theory also satisfies excision for ideals, excision for open subschemes and Zariski cohomological descent. Many known "Chern characters" on K-theory factor through KH-theory.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES MATHEMATIQUE 1987 - Tome 305 - Série I - n° 18
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