108 citations · 236 across the 36 of their papers we have counts for
39 papers
The bounds and are sharp
Emiel Lorist, Jan van Neerven
It was proved in the 1980s by Burkholder and Bourgain that, for any Banach space and , the UMD property for is equivalent to boundedness of the Hilbert tran…
Dimension-free -calculus of angle for UMD-valued Ornstein--Uhlenbeck operators
Jan van Neerven
Let , let be a UMD Banach space, let , and let be the generator of the Ornstein--Uhlenbeck semigroup on $L^p(\mathbb R^d,γ_d;…
Necessary conditions for deterministic and stochastic maximal regularity
Emiel Lorist, Jan van Neerven, Mark Veraar +1
We study the role of Banach space geometry in deterministic and stochastic maximal regularity. We first construct an example showing that the UMD assumption in the characterisation…
A Bismut-Elworthy-Li formula for linear stochastic evolution equations in Banach spaces
Jan van Neerven
We prove a Bismut-Elworthy-Li formula for linear stochastic evolution equations in Banach spaces. The admissible directions are those for which the deterministic orbit is square in…
Holevo classicalisation and context integration: Global versus protocolwise integration
Jan van Neerven, Marijn Waaijer
Suppose that a family of commutative measurement contexts is given, together with the corresponding classical probability laws. We study the problem under what conditions these con…
Lévy measures on Banach spaces
Jan van Neerven, Markus Riedle
We establish an explicit characterisation of Lévy measures on both -spaces and UMD Banach spaces. In the case of -spaces, Lévy measures are characterised by an integrabil…
Delayed choice experiments: An analysis in forward time
Marijn Waaijer, Jan van Neerven
In this article, we present a detailed analysis of two famous delayed choice experiments: Wheeler's classic gedanken-experiment and the delayed quantum eraser. Our analysis shows t…
Thermal time as an unsharp observable
Jan van Neerven, Pierre Portal
We show that the Connes-Rovelli thermal time associated with the quantum harmonic oscillator can be described as an (unsharp) observable, that is, as a positive operator valued mea…
Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices
Jan van Neerven, Pierre Portal, Himani Sharma
We consider operators acting on a UMD Banach lattice that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\fr…
Functional Analysis
Jan van Neerven
In this second edition, I have taken the opportunity to improve the presentation in several places, to test and revise the problem sets, and to add some new material.
Maximal estimates for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations
Jan van Neerven, Mark Veraar
This paper presents a survey of maximal inequalities for stochastic convolutions in -smooth Banach spaces and their applications to stochastic evolution equations.
Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes
Jan van Neerven, Mark Veraar
We prove a new Burkholder-Rosenthal type inequality for discrete-time processes taking values in a 2-smooth Banach space. As a first application we prove that if $(S(t,s))_{0\leq s…
On conditional expectations in L^p(mu;L^q(nu;X))
Qi Lu, Jan van Neerven
Let and be probability spaces, let be a sub--algebra of the product -algebra , let be…
From Modular to Distributed Open Architectures: A Unified Decision Framework
Babak Heydari, Mohsen Mosleh, Kia Dalili
This paper introduces a conceptual, yet quantifiable, architecture framework by extending the notion of system modularity in its broadest sense. Acknowledging that modularity is no…
On the constant in a transference inequality for the vector-valued Fourier transform
Dion Gijswijt, Jan van Neerven
The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of s…
Second quantisation for skew convolution products of infinitely divisible measures
David Applebaum, Jan van Neerven
Suppose and are infinitely divisible Radon measures on real Banach spaces and , respectively and let be a Borel measurable mappin…
On the R-boundedness of stochastic convolution operators
Jan van Neerven, Mark Veraar, Lutz Weis
The -boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of…
The L^p-Poincaré inequality for analytic Ornstein-Uhlenbeck operators
Jan van Neerven
Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in…
Poisson stochastic integration in Banach spaces
Sjoerd Dirksen, Jan Maas, Jan van Neerven
We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non…
Compactness in the Lebesgue-Bochner spaces L^p(μ;X)
Jan van Neerven
Let (Ω,μ) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L…
Second quantisation for skew convolution products of measures in Banach spaces
David Applebaum, Jan van Neerven
We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that unde…
Stochastic integration in Banach spaces - a survey
Jan van Neerven, Mark Veraar, Lutz Weis
This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are…
Maximal gamma-regularity
Jan van Neerven, Mark Veraar, Lutz Weis
In this paper we prove maximal regularity estimates in "square function spaces" which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particula…
The stochastic Weiss conjecture for bounded analytic semigroups
Jamil Abreu, Bernhard Haak, Jan van Neerven
Suppose -A admits a bounded H-infinity calculus of angle less than pi/2 on a Banach space E with Pisier's property (alpha), let B be a bounded linear operator from a Hilbert space…