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In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors.
We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.
We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.
Analytic cocycles of type over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.
This paper deals with approximation numbers of the compact trace operator of an anisotropic Besov space into some Lp-space,trΓ: Bpps,a (Rn) → Lp(Γ), s > 0, 1 < p < ∞,where Γ is an anisotropic d-set, 0 < d < n. We also prove homogeneity estimates, a homogeneous equivalent norm and the localization property in Bpps,a.
Using the ratio ergodic theorem for a measure preserving transformation in a -finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.
Soit un nombre de Pisot de degré ; nous avons montré précédemment que l’endomorphisme du tore dont est valeur propre est facteur du -shift bilatéral par une application continue ; nous prouvons ici (théorème 1) que l’application conserve l’entropie de toute mesure invariante sur le -shift. Ceci permet de définir l’entropie d’un nombre dans la base et d’en étudier la stabilité. Nous généralisons également des résultats de Kamae, Rauzy et Bernay.
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