scholarly journals The $L^{2}$ boundedness condition in nonamenable percolation

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Tom Hutchcroft
Keyword(s):  
Boundedness Condition

Darboux chart on projective limit of weak symplectic Banach manifold

2015 ◽  
Vol 12 (07) ◽  
pp. 1550072 ◽  
Author(s):  
Pradip Mishra
Keyword(s):  
Banach Space ◽  
Symplectic Structure ◽  
Reflexive Banach Space ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Banach Manifold ◽  
Boundedness Condition ◽  
Projective System ◽  
Banach Manifolds

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.

A martingale approach to the PASTA property

1993 ◽  
Vol 30 (01) ◽  
pp. 252-257
Author(s):  
Michael Scheutzow
Keyword(s):  
Poisson Process ◽  
Queueing Theory ◽  
Point Processes ◽  
Law Of Large Numbers ◽  
Boundedness Condition ◽  
Martingale Approach ◽  
Large Numbers ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Image Position

It is known (Weizsäcker and Winkler (1990)) that for bounded predictable functions H and a Poisson process with jump times exists almost surely, and that in this case both limits are equal. Here we relax the boundedness condition on H. Our tool is a law of large numbers for local L 2-martingales. We show by examples that our condition is close to optimal. Furthermore we indicate a generalization to point processes on more general spaces. The above property is called PASTA (‘Poisson arrivals see time averages') and is heavily used in queueing theory.

On Semipositone Non-Local Boundary-Value Problems with Nonlinear or Affine Boundary Conditions

2016 ◽  
Vol 60 (3) ◽  
pp. 635-649 ◽  
Author(s):  
Christopher S. Goodrich
Keyword(s):  
Existence Result ◽  
Boundary Value ◽  
Growth Conditions ◽  
Compact Set ◽  
Boundedness Condition ◽  
Local Boundary ◽  
Semipositone Problem ◽  
Non Local ◽  
Image Position ◽  
Special Case

AbstractWe consider the boundary-value problemwhereH: [0,+∞) → ℝ andf: [0, 1] × ℝ → ℝ are continuous and λ > 0 is a parameter. We show that ifHsatisfies a boundedness condition on a specified compact set, then this, together with an assumption thatHis either affine or superlinear at +∞, implies existence of at least one positive solution to the problem, even in the case where we impose no growth conditions onf. Finally, since it can hold thatf(t, y) < 0 for all (t, y) ∈ [0, 1]×ℝ, the semipositone problem is included as a special case of the existence result.

Cauchy and Poisson integral representations for ultradistributions of compact support and distributional boundary values

1981 ◽  
Vol 91 (1-2) ◽  
pp. 49-62 ◽  
Author(s):  
R. S. Pathak
Keyword(s):  
Analytic Function ◽  
Growth Condition ◽  
Compact Support ◽  
Analytic Functions ◽  
Convex Cone ◽  
Integral Representations ◽  
Boundary Values ◽  
Cauchy Integral ◽  
Boundedness Condition ◽  
Poisson Integrals

SynopsisUltradistributions of compact support are represented as the boundary values of Cauchy and Poisson integrals corresponding to tubular radial domains Tc' =ℝn + iC', C'⊂⊂C, where C is an open, connected, convex cone. The Cauchy integral of is shown to be an analytic function in TC' which satisfies a certain boundedness condition. Analytic functions which satisfy a specified growth condition in TC' have a distributional boundary value which can be used to determine an distribution.

scholarly journals On the Global Gaussian Lipschitz Space

2017 ◽  
Vol 60 (3) ◽  
pp. 707-720 ◽  
Author(s):  
Liguang Liu ◽  
Peter Sjögren
Keyword(s):  
Euclidean Space ◽  
Preceding Paper ◽  
Lipschitz Space ◽  
Continuity Condition ◽  
Poisson Integral ◽  
Boundedness Condition ◽  
Bounded Functions ◽  
Similar Inequality ◽  
Logarithmic Growth

AbstractIt is well known that the standard Lipschitz space in Euclidean space, with exponent α ∈ (0, 1), can be characterized by means of the inequality , where is the Poisson integral of the function f. There are two cases: one can either assume that the functions in the space are bounded, or one can not make such an assumption. In the setting of the Ornstein–Uhlenbeck semigroup in ℝn, Gatto and Urbina defined a Lipschitz space by means of a similar inequality for the Ornstein–Uhlenbeck Poisson integral, considering bounded functions. In a preceding paper, the authors characterized that space by means of a Lipschitz-type continuity condition. The present paper defines a Lipschitz space in the same setting in a similar way, but now without the boundedness condition. Our main result says that this space can also be described by a continuity condition. The functions in this space turn out to have at most logarithmic growth at infinity.

Sign in / Sign up

Export Citation Format

Share Document