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van Neerven, J.M.A.M. (author), Portal, Pierre (author)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 measure. We furthermore present extensions of this result to the free massless relativistic particle in one dimension and to a hypothetical physical system whose...journal article 2024
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Waaijer, Marijn (author), van Neerven, J.M.A.M. (author)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 that the outcomes of both experiments can be fully explained on the basis of the information collected during the experiments using textbook quantum mechanics only....journal article 2024
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van Neerven, J.M.A.M. (author), Portal, Pierre (author), Sharma, Himani (author)We consider operators acting on a UMD Banach lattice X that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator (Formula Presented) acting on L<sup>2</sup>(R<sup>d</sup>). More precisely, we consider abstract harmonic oscillators of the form (Formula Presented) for tuples of...journal article 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)In this chapter we address a couple of topics in the theory of H<sup>∞</sup>-calculus centering around the question what can be said about an operator of the form A+B when A and B have certain “good” properties such as being (R-)sectorial or admitting a bounded H<sup>∞</sup>-calculus.book chapter 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)This chapter presents an in-depth study of several classes of vector-valued function spaces defined by smoothness conditions.book chapter 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)In this chapter we address two strongly interwoven topics: How to verify the boundedness of the H<sup>∞</sup>-calculus of an operator and how to represent and estimate its fractional powers. For concrete operators such as the Laplace operator or elliptic partial differential operators, the fractional domain spaces can often be identifed with...book chapter 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)Before addressing this question for the Calderón{Zygmund type operators of the kind studied in Chapter 11, we investigate a number of related objects in a simpler dyadic model. Besides serving as an introduction to some of the key techniques, it turns out that these dyadic operators can be, and will be, also used as building blocks of the...book chapter 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)As we have seen in the preceding sections, in the context of inhomogeneous linear evolution equations, maximal regularity enables one to set up an isomorphism between the space of data (initial value and inhomogeneity) and the solution space.book chapter 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)The mapping properties of T will of course heavily depend on the assumptions made on the kernel K that we will discuss in more detail in this chapter.book chapter 2023
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Hytönen, Tuomas (author), van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, Lutz (author)In this chapter, we complement the discussion of three major themes of Fourier analysis that we have studied in the previous Volumes.book chapter 2023
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van Neerven, J.M.A.M. (author), Veraar, M.C. (author)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)) <sub>⩽</sub><sub>s</sub><sub>≤</sub><sub>t</sub><sub>⩽</sub><sub>T</sub> is a C-evolution family of contractions on a 2-smooth Banach space X and (Wt)t∈[0,T] is a...journal article 2021
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Waaijer, Marijn (author), van Neerven, J.M.A.M. (author)We present an analysis of the Frauchiger–Renner Gedankenexperiment from the point of view of the relational interpretation of quantum mechanics. Our analysis shows that the paradox obtained by Frauchiger and Renner disappears if one rejects promoting one agent’s certainty to another agent’s certainty when it cannot be validated by records...journal article 2021
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van Neerven, J.M.A.M. (author), Veraar, M.C. (author)This paper presents a survey of maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and their applications to stochastic evolution equations. This article is part of the theme issue 'Semigroup applications everywhere'.review 2020
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Cox, Sonja (author), Hutzenthaler, Martin (author), Jentzen, Arnulf (author), van Neerven, J.M.A.M. (author), Welti, Timo (author)We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process that is strongly Hölder continuous in time, then this sequence converges in the strong sense even with respect to much stronger Hölder norms and the convergence rate is essentially reduced by the Hölder...journal article 2020
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van Neerven, J.M.A.M. (author), Portal, Pierre (author)We generalise the classical Weyl pseudo-differential calculus on R<sup>d</sup> to the setting of two d-tuples of operators A = (A<sub>1</sub>,..., A<sub>d</sub>) and B = (B<sub>1</sub>,..., B<sub>d</sub>) acting on a Banach space generating bounded C0-groups satisfying the Weyl canonical commutation relations. We show that the resulting Weyl...journal article 2020
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Lü, Qi (author), van Neerven, J.M.A.M. (author)Let (A, A, μ) and (B, B, ν) be probability spaces, let F be a sub-σ-algebra of the product σ-algebra A× B, let X be a Banach space and let 1 < p, q< ∞. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to F defines a bounded linear operator from L <sup>p</sup> (μ; L <sup>q</sup> (ν; X)...journal article 2019
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Lü, Qi (author), van Neerven, J.M.A.M. (author)Extending results of Pardoux–Peng and Hu–Peng, we prove well-posedness results for backward stochastic evolution equations in UMD Banach spaces.book chapter 2019
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van Neerven, J.M.A.M. (author), Portal, Pierre (author)In this paper, we introduce a Weyl functional calculus a↦a(Q,P) for the position and momentum operators Q and P associated with the Ornstein-Uhlenbeck operator L=−Δ+x⋅∇, and give a simple criterion for restricted Lp-Lq boundedness of operators in this functional calculus. The analysis of this non-commutative functional calculus is simpler than...journal article 2018
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van Neerven, J.M.A.M. (author), Versendaal, R. (author)We prove R-bisectoriality and boundedness of the (Formula presented.)-functional calculus in (Formula presented.) for all (Formula presented.) for the Hodge–Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry–Emery Ricci curvature on k-forms.journal article 2018
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Cornelissen, Gunther (author), van Neerven, J.M.A.M. (author)On April 12th, 2017, Gunther Cornelissen and Jan van Neerven interviewed Ken Ribet at the occasion of him winning the Brouwer Medal 2017.journal article 2017