Fonctions cosinus hilbertiennes bornées dans les groupes commutatifs localement compacts
Group representations of bounded cosine functions.
Sur un théorème de Day, un théorème de Mazur-Orlicz et une généralisation de quelques théorèmes de Silverman
On some distal functions
Erratum à l'article "Sur un théorème de Day, un théorème de Mazur-Orlicz et une généralisation de quelques théorèmes de Silverman" (Colloquium Mathematicum 50 (1986), 257-262)
An analogue of the argument theorem of Bohr and its application
On some functional equation generalizing Cauchy's and d'Alembert's functional equations
Sur certains éléments ergodiques dans
On group decompositions of bounded cosine sequences
A two-sided sequence with values in a complex unital Banach algebra is a cosine sequence if it satisfies for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence is bounded if . A (bounded) group decomposition for a cosine sequence is a representation of c as for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, here referred...
On operator-valued cosine sequences on UMD spaces
A two-sided sequence with values in a complex unital Banach algebra is a cosine sequence if it satisfies for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence is bounded if . A (bounded) group decomposition for a cosine sequence is a representation of c as for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, the so-called...
Multiplier algebras, Banach bundles, and one-parameter semigroups
A characterisation of the circle group.
Some monotonicity and limit results for the regularised incomplete gamma function
Letting P(u,x) denote the regularised incomplete gamma function, it is shown that for each α ≥ 0, P(x,x+α) decreases as x increases on the positive real semi-axis, and P(x,x+α) converges to 1/2 as x tends to infinity. The statistical significance of these results is explored.
Weak compactness and summability
Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space
We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets of all bounded...
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