Inégalités isopérimétriques et inégalités de Faber-Krahn
Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes
Inequalities and interpolation.
Some examples of the close interaction between inequalities and interpolation are presented and discussed. An interpolation technique to prove generalized Clarkson inequalities is pointed out. We also discuss and apply to the theory of interpolation the recently found facts that the Gustavsson-Peetre class P+- can be described by one Carlson type inequality and that the wider class P0 can be characterized by another Carlson type inequality with blocks.
Inequalities for a regular polygon in spaces
Inequalities for differentiable reproducing kernels and an application to positive integral operators.
Inequalities for exponentials in Banach algebras
For commuting elements x, y of a unital Banach algebra ℬ it is clear that . On the order hand, M. Taylor has shown that this inequality remains valid for a self-adjoint operator x and a skew-adjoint operator y, without the assumption that they commute. In this paper we obtain similar inequalities under conditions that lie between these extremes. The inequalities are used to deduce growth estimates of the form for all , where and c, s are constants.
Inequalities for Fourier transforms
Inequalities for Jacobians: interpolation techniques
Inequalities in additive -isometries on linear -normed Banach spaces.
Inequalities in rearrangement invariant function spaces
Inequalities in Von Neumann Algebras
Inequalities involving the inner product.
Inequalities of the Kahane-Khinchin type and sections of -balls
We extend Kahane-Khinchin type inequalities to the case p > -2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces that embed in , p > -2.
Inequilogical spaces, directed homology and noncommutative geometry.
Inequivalence of Wavelet Systems in and
Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces and are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in is also shown.
Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature.
We show how an operation of inf-convolution can be used to approximate convex functions with C1 smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.
Infinite -tensor product algebras.
Infinite asymptotic games
We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity...
Infinite Asymptotic Games and (*)-Embeddings of Banach Spaces
We use methods of infinite asymptotic games to characterize subspaces of Banach spaces with a finite-dimensional decomposition (FDD) and prove new theorems on operators. We consider a separable Banach space X, a set of sequences of finite subsets of X and the -game. We prove that if satisfies some specific stability conditions, then Player I has a winning strategy in the -game if and only if X has a skipped-blocking decomposition each of whose skipped-blockings belongs to . This result implies that...
Infinite dimensional extension of A. P. Calderòn's theorem on positive semidefinite biquadratic forms.