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 Bulletin des Sciences MathamatiquesJournal Prestige (SJR): 0.96 Citation Impact (citeScore): 1Number of Followers: 4      Subscription journal ISSN (Print) 0007-4497 - ISSN (Online) 0007-4497 Published by Elsevier  [3200 journals]
• Sous-groupes réductifs canoniques de groupes biparaboliques
réels
• Abstract: Publication date: August 2019Source: Bulletin des Sciences Mathématiques, Volume 154Author(s): Nabila DjebaliRésuméNous associons à chaque sous-groupe biparabolique d'un groupe classique réel un graphe de méandres. Nous décrivons alors en termes du graphe de méandres associé les classes de conjugaison des facteurs réductifs d'un sous-groupe biparabolique d'un groupe classique réel différent de SO(p,q) et déterminons ceux de ces sous-groupes biparaboliques qui admettent des séries discrètes modulo le centre du groupe classique ambiant. We associate a meander graph to each biparabolic subgroup of a real classical group. Then, we give a description in terms of the associated meander graph of the conjugacy classes of the canonical reductive subgroups of a biparabolic subgroup in case the classical group is distinct from SO(p,q) and also determine when such a biparabolic subgroup has discrete series modulo the center of the ambient classical group.

• On the Markov commutator
• Abstract: Publication date: August 2019Source: Bulletin des Sciences Mathématiques, Volume 154Author(s): Laurent Miclo The Markov commutator associated to a finite Markov kernel P is the convex semigroup consisting of all Markov kernels commuting with P. Its interest comes from its relation with the hypergroup property and with the notion of Markovian duality by intertwining. In particular, it is shown that the discrete analogue of the Achour-Trimèche's theorem, asserting the preservation of non-negativity by the wave equations associated to certain Metropolis birth and death transition kernels, cannot be extended to all convex potentials. But it remains true for symmetric and monotone potentials which are sufficiently convex.

• Schwarz type Lemmas and a Landau type theorem of functions satisfying the
biharmonic equation
• Abstract: Publication date: August 2019Source: Bulletin des Sciences Mathématiques, Volume 154Author(s): Shaolin Chen, Jian-Feng Zhu For g∈C(D‾), φ∈C(T) and f⁎∈C(T), let BHφ,g,f⁎(D) be the class of all complex-valued functions f∈C4(D) satisfying Δ(Δf)=g in the unit disk D with Δf=φ in the unit circle T and f=f⁎ in T, where Δf is the Laplacian of f. In this article, we will show that several Schwarz type lemmas for f∈BHφ,g,f⁎(D), and, by applying these results, we will establish a Landau type theorem on a subclass of BHφ,g,f⁎(D).

• Minimizing movement for a fractional porous medium equation in a periodic
setting
• Abstract: Publication date: July 2019Source: Bulletin des Sciences Mathématiques, Volume 153Author(s): L.C.F. Ferreira, M.C. Santos, J.C. Valencia-Guevara We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability measures endowed with a non-local transportation distance constructed in the spirit of the Benamou–Brenier formula. For initial periodic probability measures, we show the existence of absolutely continuous curves that are generalized minimizing movements associated to Rényi entropy. We also develop a subdifferential calculus in our setting.

• Godbillon–Vey sequence and Françoise algorithm
• Abstract: Publication date: July 2019Source: Bulletin des Sciences Mathématiques, Volume 153Author(s): Pavao Mardešić, Dmitry Novikov, Laura Ortiz-Bobadilla, Jessie Pontigo-Herrera We consider foliations given by deformations dF+ϵω of exact forms dF in C2 in a neighborhood of a family of cycles γ(t)⊂F−1(t).In 1996 Françoise gave an algorithm for calculating the first nonzero term of the displacement function Δ along γ of such deformations. This algorithm recalls the well-known Godbillon–Vey sequences discovered in 1971 for investigation of integrability of a form ω. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability for finite Godbillon–Vey sequences to the Françoise algorithm settings.

• A coarse relative-partitioned index theorem
• Abstract: Publication date: July 2019Source: Bulletin des Sciences Mathématiques, Volume 153Author(s): M. Karami, M.E. Zadeh, A. Sadegh It seems that the index theory for non-compact spaces has found its ultimate formulation in the realm of coarse spaces and K-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and interesting examples of this program. In this paper we formulate a combination of these two theorems and establish a partitioned-relative index theorem.

• On a class of unitary representations of the braid groups B 3 and B 4
• Abstract: Publication date: July 2019Source: Bulletin des Sciences Mathématiques, Volume 153Author(s): Sergio Albeverio, Slavik Rabanovich We describe a class of irreducible non-equivalent unitary representations of the braid group B3 in every dimension n≥6 which depends continuously on n2/6+1 real parameters. We show that the upper bound on the number of the parameters of which the class of irreducible non-equivalent unitary representations of B3 depends smoothly is equal to n2/4+2. The proof is achieved by a construction of such a class. We also prove that the tensor product of the Burau unitarisable representation of B4 and the irreducible unitary representation of B4 that coincide on commuting standard generators always forms irreducible unitary representations for the braid group B4. This gives a new class of unitary representations for the braid group B4 in 3n dimensions.

• An example of a capacity for which all positive Borel sets are thick
• Abstract: Publication date: July 2019Source: Bulletin des Sciences Mathématiques, Volume 153Author(s): Michał Morayne, Piotr Zakrzewski, Szymon Żeberski On the Cantor cube {0,1}N with the standard product topology we construct a finite Choquet capacity with respect to the family of all compact sets such that every compact set of positive capacity contains continuum many pairwise disjoint compact subsets of positive capacity.

• Phase space Feynman path integrals of parabolic type with smooth
functional derivatives
• Abstract: Publication date: July 2019Source: Bulletin des Sciences Mathématiques, Volume 153Author(s): Naoto Kumano-go We give two general sets of functionals for which the phase space path integrals of m-th order parabolic type (m>0) have a mathematically rigorous meaning. More precisely, for any functional belonging to each set, the time slicing approximation of the phase space path integral converges uniformly on compact subsets with respect to the final point of position paths and to the initial point of momentum paths. Each set of functionals is closed under addition, multiplication, translation, invertible linear transformation and functional differentiation. Therefore, we can produce many functionals which are phase space path integrable. Furthermore, though we need to pay attention for use, we ensure that the following operations are valid for the phase space path integrals: (1) interchange of the order with integrals with respect to time (2) interchange of the order with some limits (3) invariance under orthogonal transformations (4) invariance under translations with respect to momentum paths (5) integration by parts with respect to momentum paths.

• R n ,+ T n +and+Two+Step+Nilpotent+Lie+Groups&rft.title=Bulletin+des+Sciences+Mathamatiques&rft.issn=0007-4497&rft.date=&rft.volume=">Around Theorems of Ingham-type Regarding Decay of Fourier Transform on
R n , T n and Two Step Nilpotent Lie Groups
• Abstract: Publication date: Available online 28 February 2019Source: Bulletin des Sciences MathématiquesAuthor(s): Mithun Bhowmik, Swagato K. Ray, Suparna Sen Classical results due to Ingham, Levinson and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. We prove some analogues of these results on the n-dimensional Euclidean space, the n-dimensional torus and connected, simply connected two step nilpotent Lie groups. We also use these results to show a unique continuation property of solutions to the initial value problem for time-dependent Schrödinger equations on the Euclidean space and a class of connected, simply connected two step nilpotent Lie groups.

• On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic
operators
• Abstract: Publication date: Available online 28 February 2019Source: Bulletin des Sciences MathématiquesAuthor(s): Francesco Della Pietra, Nunzia Gavitone, Gianpaolo Piscitelli Let Ω be a bounded open set of Rn, n≥2. In this paper we mainly study some properties of the second Dirichlet eigenvalue λ2(p,Ω) of the anisotropic p-Laplacian−Qpu:=−div(Fp−1(∇u)Fξ(∇u)), where F is a suitable smooth norm of Rn and p∈]1,+∞[. We provide a lower bound of λ2(p,Ω) among bounded open sets of given measure, showing the validity of a Hong-Krahn-Szego type inequality. Furthermore, we investigate the limit problem as p→+∞.

• Elliptic Operators Associated with Groups of Quantized Canonical
Transformations
• Abstract: Publication date: Available online 24 January 2019Source: Bulletin des Sciences MathématiquesAuthor(s): A. Savin, E. Schrohe, B. Sternin Given a Lie group G of quantized canonical transformations acting on the space L2(M) over a closed manifold M, we define an algebra of so-called G-operators on L2(M). We show that to G-operators we can associate symbols in appropriate crossed products with G, introduce a notion of ellipticity and prove the Fredholm property for elliptic elements. This framework encompasses many known elliptic theories, for instance, shift operators associated with group actions on M, transversal elliptic theory, transversally elliptic pseudodifferential operators on foliations, and Fourier integral operators associated with coisotropic submanifolds.

• Rotations of convex harmonic univalent mappings
• Abstract: Publication date: Available online 9 January 2019Source: Bulletin des Sciences MathématiquesAuthor(s): Ilgiz R. Kayumov, Saminathan Ponnusamy, Le Anh Xuan Let f=h+g‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D. In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ∈[0,2π) such that the function h+eiθg is convex in D. In this article, we first disprove a more flexible conjecture: “Let f=h+g‾ be a convex harmonic mapping in the disk D. Then there is a θ∈[0,2π) such that the function h+eiθg is starlike in D”. In addition, we present an example to show that there exists a harmonic automorphism f=h+g‾ of a disk such that the function h+eiθg is convex in only one direction for θ≠0, and that the analytic function h+g is not starlike therein. The article concludes with a new conjecture.

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