Planarizable supersymmetric quantum toboggans.
Plongements radiaux à courbure de Gauss positive prescrite
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
Podal subspaces on the unit polydisk
Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(D). To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points. By the methods...
Poincaré inequalities and hitting times
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for log-concave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial,…)....
Poincaré inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups
Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient
Point fixe d'une application non contractante.
We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.
Point interactions in Lp .
Points fixes des contractions de certains faiblement compacts de
Points fixes et théorèmes ergodiques dans les espaces L¹(E)
We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.
Point-valued mappings of sets.
Pointwise absolutely convergent series of operators and related classes of Banach spaces
We study classes of operators represented as a pointwise absolutely convergent series of simpler ones, starting with rank 1 operators. In this short note we address the question, how far the repetition of this procedure can lead.
Pointwise and integral estimates for the -Riesz potential in terms of -maximal and -fractional maximal functions.
Pointwise asymptotics for the jumps of ergodic averages.
Pointwise convergence of nonconventional averages
We answer a question of H. Furstenberg on the pointwise convergence of the averages , where U and R are positive operators. We also study the pointwise convergence of the averages when T and S are measure preserving transformations.
Pointwise ergodic theorems and function classes
Pointwise ergodic theorems for functions in Lorentz spaces with p ≠ ∞
Let τ be a null preserving point transformation on a finite measure space. Assuming τ is invertible, P. Ortega Salvador has recently obtained sufficient conditions for the almost everywhere convergence of the ergodic averages in with 1 < p < ∞, 1 < q < ∞. In this paper we obtain necessary and sufficient conditions for the almost everywhere convergence, without assuming that τ is invertible and only assuming that p ≠ ∞.
Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations
Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized and unified...
Pointwise ergodic theorems with rate and application to the CLT for Markov chains
Let T be Dunford–Schwartz operator on a probability space (Ω, μ). For f∈Lp(μ), p>1, we obtain growth conditions on ‖∑k=1nTkf‖p which imply that (1/n1/p)∑k=1nTkf→0 μ-a.e. In the particular case that p=2 and T is the isometry induced by a probability preserving transformation we get better results than in the general case; these are used to obtain a quenched central limit theorem for additive functionals of stationary ergodic Markov chains, which improves those of Derriennic–Lin and Wu–Woodroofe....