The Hahn-Banach theorem implies the Banach-Tarski paradox
The Hahn-Vitali-Saks and the uniform boundedness theorem in topological groups.
The heat kernel on Lie groups.
The Helgason-Fourier transform for symmetric spaces. II.
The Herz-Schur multiplier norm of sets satisfying the Leinert condition
It is well known that in a free group , one has , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for .
The infinite Brownian loop on a symmetric space.
The Injection and the Protection Theorem for Spectral Sets
The invariance principle for random variables with values in locally compact groups
The irreducible unitary -spherical representations of
The Levi-Civita equation, vector modules and spectral synthesis
The purpose of this paper is to give a survey on some recent results concerning spectral analysis and spectral synthesis in the framework of vector modules and in close connection with the Levi-Civita functional equation. Further, we present some open problems in this subject.
The Lévy continuity theorem for nuclear groups
Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited...
The Lévy-Khintchine-Formula for Dissipative Distributions.
The local weight of an effective locally compact transformation group and the dimension of
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The L...-representation algebra of a foundation topological semigroup.
The L...-representation algebra of an idempotent topological semigroup.
The Maximal (C, ...) Operator of Two-Parameter Walsh-Fourier Series.
The method of Grothendieck-Ramirez and weak topologies in C(T)
The minimum existence of functional
The Minlos lemma for positive-definite functions on additive subgroups of
Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let (resp. ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...